The curious reader might be interested to know that Diophantus and the Greek thinkers rejected the concept of negative numbers (and irrational numbers, of course) as “patently ridiculous” and “idiotic.” And we are a Greek-based society. So to borrow David Hume’s plaintive question – Then whence Negative Numbers? The answer to this question lies in the Orient. If there was ever a “yellow menace,” negative numbers are it. The Chinese, the Indians, and the Muslims gave us negative numbers. Not the superior Greeks. Is this a coincidence? I think not. These countries have had a vested interest in the concept from the very beginning.

Fortunately, however, negative numbers are behind a very thin conceptual veil. Once removed, it is easy to see the “Chinaman behind the curtain.” I’ll just say QUED ahead of time. Observe:

I can have three horses, but I cannot have negative three horses. Some people, suffering from Cognitive Dissonance (CD), suggest that “debt” is a manifestation of negative numbers. But that’s really just arguing semantics. Wittgenstein and Derrida disproved semantics back in the 20th century. In any case, what’s really going on in the situation is not that I have negative horses; rather, I owe some positive horses (Positive horses=horses that exist; countable horses. Who would want to be owed imaginary horses?). We can get by just fine without negative numbers. Besides, the Universe is full of stuff, not -stuff. If you would like to confirm this, here is the relevant empirical experiment:

Turn your head this way and that, and look at things. You may if you wish do this in a lab, for a more sciencey feel.

This conclusion, in conjunction with the abolition of infinity, has pathbreaking – nay, watershed – consequences for the number line, which now looks like this:

I constantly get compliments for how incredibly parsimonious my arguments are – well, this one perhaps beats them all!

If the abolition of negative numbers in the conceptual schema catches on in the West, we can expect an end to the Three Thousand Year Reich of the Neo-Zoroastrians who think that the number line is an *exact* balance between negative and positive (seriously, what are the chances anyway that it would be an exact balance? It’s even worse than 1/Penultimate. It’s zero!). Now some might say that empirically the Universe *is *symmetrical, and they might cite anti-matter as confirmation of this. But there is not room here to discuss anti-matter; I’ll leave that for a future post!

I cannot believe that while rightfully attacking the infidels negative numbers you persist in using their even more nefarious tool. Zero like negative numbers infected us from the east and MUST be stopped.

Dear Edmund Harriss:

It’s about time you commented here!

You know, it’s interesting: I KNEW this would come up. BUT I tend to be okay with the concept of zero. You might be surprised, but it’s the truth.

Anyone who has experienced loneliness and loss has experienced zero. Furthermore, my arguments would not be applicable to zero. You can have zero horses, for example.

Lastly, I have a developing theory about the existence of non-absolute numbers (e.g. 0.7) being relative to the absolute numbers that encompass them. But for this to work for the countable numbers less than 1, zero also has to exist! There are still some rough edges on the theory, but it’s one of the reasons why I hold on to zero, despite the number’s dubious origins.

NS

Even the number 1 is not to be trusted!

http://dreadtomatoaddiction.blogspot.com/2008/10/2-is-1.html

So say you define the point where you’re standing now as 0. One step forward is defined as +1 and so forth.

Your contention is that no matter where you are, you will never be able to take a step backwards, which would constitute being at -1?

You are either an emu, a kangaroo or with your back against a wall.

Not to mention just plain stupid. A number plane is about relativism, look at such concepts as energy. The total amount of energy in a chemical compound is not known, but we can measure the change in energy between different states. The relative energy between one state and another are all that count for our purposes, and a similar attitude should be taken with the one dimensional number plane.

Just as an aside, if you are familiar with projectile motion equations you will no doubt be aware of this little phenomenon.

When something is launched from a height, working out the distance travelled produces a +’ve and -‘ve answer. The positive answer is the distance travelled. The negative answer is the position from which parabola described by the projectile would intersect the x axis if it is extended behind the launch point, and shows where the projectile would have been launched from if it were at zero elevation and landed in the same position as the projectile launched from a height.

This just goes to show how negative numbers can relate to reality, disproving your zero horses arguement.

You must really hate imaginary numbers. A shame they are the only way to calculate the behaviour of electrical circuits to any advanced degree.

Again, the author criticizes the negative number paradigm by making up some notion of negative numbers that no one holds. I also want to point out that his literary knowledge is clearly irrelevant to his mathematical reasoning. Probability, negative numbers, imaginary numbers; no one holds these as things that actually exist in reality. In fact, no one holds that numbers themselves actually exist in reality! The number -2 does not exist in reality anywhere; neither does having 2 stones make the positive number 2 exist. They are all symbols to allow reasoning to occur, and no one has ever said they were more than that. What is he talking about?

You’re spot on about negative numbers, but I think you’ve managed to confuse yourself about zero.

Try this experiment: put two apples in a box. Take one out– how many apples are left? At this point it’s right and proper to say that there is one apple. But what happens when you take that apple out? You might be tempted to say that there are zero apples in the box now. But ask yourself this question: what test could we perform on the box to determine that there are zero *apples*? That is, the emptiness, or ‘zeroness’ of the box doesn’t have a type. It doesn’t have “zero apples”, it’s just empty.

The concept of zero is bankrupt for this reason: it’s not grounded to anything, but rather contains some sort of metaphysical infinity of types. If we permit the box to contain zero apples, it must contain zero unicorns and zero aircraft carriers as well; an inconceivable infinity of zero things that it contains.

Furthermore, the number line makes no sense. Without zero, it naturally goes like this (if we’re talking about apples):

1 (apple) – 2 (apples) – 3 (apples) … P (apples)

If we add in zero we get this ridiculous situation:

0 (everything?!) – 1 (apple) …

Your theory of non-absolute values needs a smallest number to function. After all, the idea that numbers can get arbitrarily small is just the tyranny of infinity in the reciprocal. There has to be some number which is smaller than all the others, but is still conceptually sound (i.e., is not “zero”).

Mrs. Padraigh,

Your first post is confused, and the second is derived from it. The pitiful examples you cite are straightforwardly metaphorical. We could substitute any “x” for the negative symbology.

How dare you criticize my horses argument?

NS

Jason,

You write:

Your ignorance of philosophy is wide, deep, and vast. There are many realists about numbers. But even so, it turns out you agree with me about the bulk of my post!

Strictly speaking I would say negative numbers fail as “symbols” in your sense, since they signify nothing.

NS

Rand,

Your comment is elegant and profound, causing many tremors in the otherwise placid landscape of my thought. I will think on your inspired proof, and hopefully dedicate a post to it.

NS

Look, your debts aren’t going to magically disappear no matter how much you rant about the unreality of negative numbers.

Dear Myrmidon:

What I offer is a reinterpretation of debt; as Hegel said, “[W]e have two tasks: not only to change, but to interpret, the world.”

What I offer is a reinterpretation, a reconceptualization if you will, of debt. I owe positive money, I don’t have negative money. I don’t have negative zebras either.

However, I must take into account the beautiful ponderings of Rand in the comment above. This is forthcoming.

Yours,

NS

Or we could just leave it as it is and stop obsessing over stupidly minor shit.

+1 and -1

mulplication/division

squaring/square root

notice this operation cancels each other out.

this is what they don’t want you to know. math is related to symmetry, which is a really SIMPLE concept.

I cannot believe this website even exists. Seriously the height of stupidity is to deny something as fundamental to modern science and math as non-positive numbers. All of you who believe such wholly unintelligent ideas really are a waste.

Your position that the Greeks were superior is laughable. They believed that a man drove a chariot driven by fire horses to bring day about.

We base modern science on the rights and wrongs of the ancient and long-forgotten civilizations.

Without zeros and negative numbers, you wouldn’t even be able to post this anti-intellectual nonsense.

So, by your logic, what is the answer to 3-5?

Hi Doubtyoucare. Thanks for stopping by and reading through my findings.

However, I can’t seem to find any numbered questions in the discussion above. Could you refer me to what you are talking about?

NS

CBRodriguez,

You claim that my position is self-defeating, because my very posting depends on zeros and negative numbers. Yet, where do I question the concept of zero? Your false accusation is as outlandish as it is unjustified.

I accept zeros. And I also accept ones. Those are the only numbers I need for the gematria of computer magic to operate.

NS

Joe,

A simple name for a simple woman.

You write,

This is very true. But I don’t think your examples are symmetrical. Rather, they are apposed!

NS

I’m not really referring to anything previously stated. I just feel that before you criticise negative numbers, you should answer the simple questions such as:

3-5

And also, how much important maths, such as quadratics (if negative numbers don’t exist, how could one use quadratic formula in the case of x^2-6x+6 if you refuse to accept that b=-6) can rely on foundations built entirely on positive numbers.

Finally, what is your proposed alternative to negative numbers? Surely there must be some simple notation to say “You owe one pound.”

At every point of criticism you seem to become either defensive or dismissive. Rarely do you offer a true rebuttal of counterpoints offered. “You sir are no scholar” or something to that effect seems to be a favorite phrase of yours. A true “scholar” by most definitions, would not respond they way that you do.

I must admit I was originally intrigued but as I read more of your posts I noticed an ugly pattern. Do you have any idea what a neo-Zoroastrian is? I’m actually Zoroastrian, so please don’t even pretend you really know what you’re talking about here. Using large, esoteric and complex sounding words is no way to impress or convince people.

Numbers are an idea, a concept, if you limit them to representing “real” things, then you severely limit their usefulness. As an engineer, I fully appreciate the relevance of negative numbers, imaginary numbers and the concept of infinity. They are a tool. I also can’t *realistically* have 10^5000000000 horses, because that many horses do not actually exist. Are you saying that that “number” also does not exist?

That pill you take when you have a headache, that car you drive and above all, that computer you use to spout your thoughts to the world, were all designed thanks to some very useful concepts, numbers, yes negative ones. If all you’re interested in is the “counting numbers” then I feel you should stick to counting horses. Simply put if your “proofs” were correct, then the website that you post on, could not exist.

Our number system is largely based from Indian maths that were borrowed by Islam who introduced it to the West. The ancient Greek maths was constructed to study geometry, whereas the Eastern system of maths was constructed also to study algebra.

The West adopted the Eastern style of maths because it was easier to perform calculations.

Arguing we should reject negative numbers because they’re not Greek (who used numbers to measure areas and not beyond that) is as ridiculous as rejecting zero because the Greeks rejected it. Also an Indian concept.

If debt can be correctly reinterpreted into positive numbers, then in what way are the negatives an ancient evil Eastern conspiracy? Money is still owed in some direction or other.

And why the hell are you writing in English?

I hadn’t visited this post in over two years (Post #3, under my verisimilinym). How delightful to see that the discussion continues to grow.

Yes tomato man, isn’t it truly something? ? The bees continue to gather to the honey!

NS

What, exactly, is 1-2, if there is no such thing as a negative number?

Oh, and by the way, what if, instead of saying that negative numbers are a liberal conspiracy because they are not Greek, we judge the existence of negative numbers against the disbelief of the Greeks, and pass judgment on the Greeks themselves.

Oh, and if everything coming out of Asia is an evil scam, then what do you say to the Chinese invention of, let’s see:

paper

printing

the compass

the bell

the coffin

the fork

chopsticks

lacquer

the cultivation of millet

noodles

oars

triangular plowshares

rice

the banknote,

and others which I don’t have time to list.

Wow, I don’t really think you’ll enjoy going without all those nasty, evil, “yellow menaces”.

I thought that humanity had sort of come to an agreement about this: the reason that what science says is taken as truth, is because, gasp, there are scientists checking it. OK? Are we clear?

>”the reason that what science says is taken as truth, is because, gasp, there are scientists checking it.”

That simply cannot be so. Scientists check far more false things than true things. It is not the act of checking that makes it true.

Yes, I’m sure they do.

But guess what? Those false things don’t end up being taught!

I never suggested that the act of checking makes something true. I said that the teachings of science are taken as truth because they were checked, AND passed the check. That’s why just about everyone accepts negative numbers.

Also you still haven’t responded to the two other parts of my comment.

Another argument, by the way: if you owe 3 dollars and paying the three dollars makes you owe nothing and have nothing, then you end up with zero. Therefore, x+3=0 if x is the amount of money you start with. 0-3=…..-3. There’s just no other way to solve something like that.

Well, no – false things are taught all the time too, though we might hope these are informed falsehoods with only a small margin of untruth. Your first post was rather ambiguous, and all I did was make that ambiguity obvious. Your second post improves the situation only slightly. Will you get it right on the third try?

I did not respond to the other two parts of you comment because it is not my blogs. Also, I generally don’t comment on punctuation.

@NS: The snowflakes are pretty, but they make it hard to come back to the comments box after scrolling up.

Alright, well let’s take a roster. I made three arguments, and you made a straw man to defeat one of them. I clarified. Then, you posted to insult me.

The other two parts, the main parts of my argument, in addition, I would argue, to the third part, still stand entirely.

Oh wait. Make that four, if you count my most recent one.

Does directly addressing my arguments harm you?

A roster? At the moment that would be just the two of us.

Apologies for any insult. I honestly find some of your statements to be flawed or not clearly worded, and I do not care to interpret what you might be trying to say. There is a point to this blog, and it has a lot to do with the flawed thinking that most intelligent folk take for granted. Our host is a master at taking these flaws and throwing them back in ways we cannot ignore. If you do not understand, then I suggest you start by reading about Poe’s Law.

Oh, oops. An inventory. I misspoke.

Now since when is it reasonable to toss out an argument without bothering to understand it, as you admit to doing?

I think that any blog that thinks it can “defeat” science and math has more to do with ignorance than innovation. Science and math, like semantics above, are fields of study. You can’t disprove fields of study. You can disprove what people in those fields of study say, but you can’t disprove the fields of study.

Take biology, the study of life. You can disprove the current approach to it, you can disprove how we’re studying life as a viable approach to the study, but you can’t disprove biology. Biology isn’t even a statement to disprove.

By the way, considering the way you threw around Poe’s Law, I think you might be the one who doesn’t understand. Are you suggesting this blog is a sarcastic parody of ignorance, and not truly ignorant?

BTW this is what you guys sound like:

NotedScholar, where’s your noted scholasticism when someone makes a reasoned jab at your arguments?

OK just to be clear, that’s not actual scientific terminology, it’s “techno-babble”. Just thought I’d clarify that.

Dear Doubt Your Care,

First, I do care! Now onto your points.

Thank you for clarifying your initial question. My answer to the arithmetical problem three minus five is that it is undefined. Actually, this is roughly what is taught at the earliest stages of mathematical education, until children later become corrupted by magical thinking.

You ask how “much important maths” [sick] like quadratics can work. Frankly, I’ll leave that to the graduate students! But I should say that I’m not committed to the preservation of theorems that relied on negative numbers.

You ask about simple notation, and I must say that this is a theological belief many scholars have, which they shouldn’t. The world is complicated – why shouldn’t our notation reflect that?

Cheers,

NS

Dear Next to Last,

I know what Zoroasterianism is exactly – the believe that there are good numbers on the one hand, and bad numbers on the other. Furthermore, these numbers exist, and are gods.

First you say you are zoroasterian, then you say you are an engineer? I’m confused! Anyway, I agree that negative numbers can be emotionally and spiritually “relevant,” but that doesn’t mean they are real! The world is inconvenient and disappointing sometimes!

Your appeal to pills is beyond my competence. I am not a medical blog!

Best,

NS

Dear Ste,

You are correct in your historicism. I have focused on the Chinese influence (even more relevant now than a decade ago when I first posted this), but you are right to bring out the other influences.

You are right that western laziness – the very same laziness that brought us video games and obesity – is responsible for letting the Chinese create negative numbers.

I do not remember whether I have commented on “zero” on this blog, but it does seem like I can have nothing of something, as paradoxical as it might sound. Perhaps I shall pursue this topic in the future! Thanks for bringing it up.

Yours here,

NS

Lenoxus,

I’ll answer your ejaculations in order.

(1) You say, “Debt will always exist. Doesn’t matter to whom it goes.”

Wrong. Consider the following: there are five things; each of these things has one dollar; therefore, there are ten things – the original things, plus the five dollars. To get the five dollars, I apportioned one dollar to each of the things. Anyway, no debt!

(2) I am writing in English because it appears to be the official language of the Internet. When I Google search I never see other languages… so I assume this is the best one for blogging.

Today,

NS

Dear Tomato Man,

Thank you for taking care of the fulminations of Ms. Dieu de Lacunes. She is very hostile to my theories!

Your friend,

NS

Dieu de Lacunes is just confused. Given time they may outgrow this condition, we hope.

Ha wow. First of all, I’m not a woman, I’m a man, and Dieu de Lacunes is not a name. It’s French for “god of [the] gaps”, and it’s the pseudonym I use for dealing with ignorance.

Also, tomato addict, I’m not a they, and you’re not a we. Just a little grammar.

Now last I checked, I’ve made arguments most of which have gone unanswered. So I’d hardly say that my “fulminations” have been “taken care of.” Maybe it will help your comprehension if I repeat this again, in other words this time.

So first, you say that negative numbers could not be real because they’re not Greek. First of all, what makes the Greeks inherently superior? Second of all, as I noted above, the notable things you use every day that are not Greek include:

paper

printing

the compass

the bell

the coffin

the fork

chopsticks

lacquer

the cultivation of millet

noodles

oars

triangular plowshares

rice

the banknote,

and others which I don’t have time to list.

The ending to that bit is interesting to. The link is about Chinese ownership of American debt. So what’s your point? Did Chinese mathematicians 1000 years before Jesus invent negative numbers because they knew that the United States (not even known about in the Old World at the time) would one day use them to be in debt to China?

Now, about the disproofs.

If you owe three dollars to someone, then paying three dollars would make you owe and have nothing, right? Paying three dollars to someone means adding three dollars to your balance with that person. Owing nothing and having nothing means your balance with them is zero. So the starting balance +3 [the money you pay to the person]= 0[your balance at the end.

x+3=0. Solve, and you find that x=-3. It doesn’t equal undefined. Undefined plus three does not equal zero. Sorry. Negative numbers really are a way of representing debt. Your theory is that you owe positive money. As you say, that’s arguing semantics, and so it’s really the same thing, but for the sake of argument, we’ll say they’re different. What does owing positive money mean numerically? -+3? Unless that means minus positive three, in which case what are you subtracting from, then it’s a negative of a positive, which involves negatives.

As you are so fond of saying.

QED

By the way, the link that you say “disproves” semantics is a dead link. The page it links to doesn’t exist. So what was that proof again?

Ms. (/Mr.) Lacunes,

First you accuse Mr. Tomato of not addressing your arguments, which he did. Where is the problem?

But then you accuse me of

argumentatum ad Chinesum, which is aninformal, not a formal fallacy. But in any case the superiority of the Greeks is easily proved – consider, e.i., the phalanx.Also I am not aware of ever writing “qed.”

Also, but more importantly, your postmodern theory that negative numbers “represent” debt – which is not itself a number – is vague and obscurantist enough to escape direct refutation.

On the broken link, all I can say is that it used to be unbroken. Not my problem if people want to sanction me by blocking my links.

As for Chinese mathematicians trapping the West in debt, I’ve shown how. They are the chief beneficiaries of a mathematical concept which they invented – and they’ve had a continuous stream of national existence through the whole period. So there’s no need to bring in Jesus, as you inexplicably do.

As for your gender, I regularly have this problem with Angelic Plume, a regular commenter/stalker on this blog. It is weird to me that people are so concerned about appearing “male” on this blog.

Cheers,

NS

First of all, I am a male. Let’s just get that clear. I don’t care what my gender is, but I would appreciate if you would get it right. I noted my gender because you have a habit of insulting people in a discriminatory fashion for it, and so I didn’t want it to happen to me. example:

“Joe,

A simple name for a simple woman.”

So I wanted your antics to be out of the way.

As far as I can tell, tomato man only told me my arguments were flawed, without proof. If he disproved them in a serious way, please quote the section to me, and I’ll refute it.

I never accused you of any specific fallacies. I just told you that the Greek were not inherently superior, and told you that the inventions of the Chinese proved this. Now you say that the phalanx refutes this. The phalanx was a major part of warfare until the Romans defeated it and conquered the Greeks. The printing press revolutionized printing, and allowed the book to be distributed to the common man. Best of all, the printing press is one of many.

Also, if we want things of similar type, gunpowder is another weapon of war, which continues to dominate the battlefield.

Also, word of advice, it’s not e.i., it’s i.e.

Yes, you did say QED

“I’ll just say QUED[sic] ahead of time. Observe:”

Now, unless you really meant to say QUED, in which case, what on earth does that have to do with this, then that would mean QUED.

So you claim to be a scholar. Does calling something obscurantist make it wrong? Does it eliminate the need to prove it wrong? Also, why was represent in quotes? Even positive numbers can only be represented.

The link is broken. I’m not obliged to believe in a broken link. You can’t tell me that the proof used to be there, but, well, you lost track of it. Also the chances that a blog that has been visited only 94,761 times ever, mostly by the same group of people, would be noticed by someone, is unlikely. Also, the chance that that someone is the maker of the website, and that they care, is zero.

As far as the Chinese mathematicians are concerned, you think everyone Chinese is the same, and I can’t help that, but how do negative numbers benefit the Chinese? You don’t need them for debt, by your own logic, because debt can be considered the owing of positive amounts. The chinese don’t need negative numbers to own our debt. Also, I brought in Jesus so as to use a recognized dating format. I could have said 3000 years ago, or 1000 BCE, and meant the same thing.

What I’m concerned about with gender is that you’ll use gender as a smear, like you often do. Also, I value factual correctness, as you claim to, and so would hope that you could state facts such as my gender correctly.

Pseudonymously yours,

Dieu

>As far as I can tell, tomato man only told me my arguments were flawed, without proof.

I believe I said your arguments were ambiguous. In other words, not well formed, difficult to discern, poorly stated, ill-defined. I do not care to speculate about what you *might* have intended to ask, and answering the wrong question is a waste of time (but remains a popular activity, none the less). I don’t think any proof is required if there isn’t a question.

I think maybe if you were paying attention, you would have noticed that I didn’t ask a question. I made a rebuttal. Then, I made it again. So far, none of my rebuttals have been answered.

I believe I just noted that you did not ask a question – Is this incorrect?

My contribution so far has been mostly to point out some factual errors, though my previous post was more of a clarification. I am satisfied to allow our host to conduct his own rebuttals, and I do not think he really needs my assistance in that matter. Is there something more you require of me?

NS: You should consider restoring Angel Plume’s posts (if possible). Some of them are enlightening.

No it is not incorrect, and, in fact, if you wish to leave the rebuttals to noted one here, then, sure, that’s fine by me. I was just intending to clarify that such questions don’t disprove what I say.

That’s funny …

>”I don’t think any proof is required if there isn’t a question.”

… because I could have sworn I just wrote something like that. Oh well.

Your comment was in a different context, but whatever.

Anyways, noted scholar, am I sensing a trend? Is there some fact I can derive from the fact that you never respond to serious challenges to your theories?

>”Is there some fact I can derive from the fact that you never respond to serious challenges to your theories?”

That I can answer. Our host has been rather busy with other tasks lately, so the lack of a prompt response is not particularly meaningful. If you want to look for patterns, I suggest you review more than just this one post.

Notedscholar, are you aware that the Greeks didnot belive in non-whole numbers? If so, do you also advocate that they be expunged from textbooks of the future? Also, we are not a Greek based society. Our society is a meldding of Greek, Latin, Chinese, and many others. This is not a negative. “Alloy’s are stronger.”

Un,

First you say we aren’t based on the Greeks and then you immediately contradict yourself and say we are. I’ll assume this was a careless oversight, not a deep confusion in your logic.

As for whole numbers, they are certainly the most intuitive of numbers. This isn’t the point of the post, but if you want my opinion, it’s that we should believe in whole numbers and whatever we can BUILD from whole numbers.

Goodbye for right now,

NS

Debt is represented by negative numbers. If I have -3 horses, that is, generally, taken to mean that I am 3 horses in debt. Another way of writing this, is, that I owe someone three (positive) horses. Owing something is also called being in debt; the terms are interchangeable, and negative numbers are another way of saying debt. So to say that you owe three positive horses is to say you have negative (positive three) horses, or (-1 * 3) horses, or -3 horses. Negative numbers are just a way of writing debt easier. So you are correct in saying that I owe 3 horses; people choose to write that as -3. Certainly, you don’t physically have negative 3 horses in your backyard, but that is because negative numbers are not counting numbers, numbers that you can have a physical amount of; negatives are representations of debt. Also, a link in your post appears to be broken- perhaps you could find another source with similar information inside?

My sides have split. Please, tell me more, Oh Guru Of Mathematical Wisdom!!

What I said under my previous name was that we are not ONLY based on the Greeks.

I await your article on irrational numbers with great anticipation. Also, pointing out that negative numbers may not ‘exist’, but they are just as useful as any others.

Student and tutor,

It is possible that negative numbers could be a “nobel lie” in the sense of Aristotle’s belief in the equality of all animals. But that’s consistent with my point.

Best hopes,

NS

By the way, when one of the earlier commenters wrote 2-5, they were not referring to a list of questions, but meant 2 minus 5, which would be negative 3. Also, debt isn’t a manifestation of negatives, negatives are a way of representing debt.

Ihave to thank you for the efforts you have put in penning this blog.

I’m hoping to see the same high-grade blog posts by you later on as well.

In truth, your creative writing abilities has inspired me

to get my very own site now 😉

The most remarkable attribute of this theory is not the incredibly parsimonious way it has been expressed but rather the incredibly parsimonious intellect that authored it. The ultimate debate here is not about mathematics; it is about whether the author’s mother should have had an abortion. Still, it’s pleasant to see that in this case the internet ( a mathematical construct utilizing negative intergers ) has enabled even the mentally handicapped to keep busy.

FYI, our society is an amalgam of Greek, Roman, Germanic, Slavic, and Norse, with elements taken from Arabic, African, Chinese, and Japanese cultures (among others) along the way. That’s what makes America great. It is also not inherently true that the Greeks were superior. Are you forgetting Aristotle’s four elements, or the geocentric universe held to be true until Galileo, Copernicus, Brahe, and Kepler came along? The Greeks had many great ideas, but they weren’t superior. Also, while they had a problem accepting them, the Greeks also gave us a proof that irrational numbers exist. In contrast, they never considered the concept of zero, which wasn’t addressed in Europe until well after the fall of the Roman Empire. The Mayans came up with it before we did. We also use the Arabic numerala, not the Greek or Roman numerals.

Culture and history aside, negative numbers are very useful, and as they are part of a self-consistent system, they form a valid part of mathematics, whether you accept them or not. They do not have literally exist in the real world to be a vaild part of math. Your argument against them is merely one of philosophy and semantics, not formal logic or numerology. However, it should be noted that in rejecting numbers, you no longer have to worry about imaginary numbers, so good for you, I guess.

Sorry. That last sentence should have “…in rejecting negative numbers…”; my bad.

Let’s try this:

1 have $10. I give Andy $15. The expression would be 10-15. There is no other way to express the answer without negative numbers, as one cannot simply flip the sign on 1 side of the equation without flipping the sign on the other.

Negative numbers are just an IDEA; they don’t represent anything that really EXISTS, they’re just a useful concept to have. Of course you can’t have -3 horses, that doesn’t make sense. You simply have just -3; not -3 of any object, just -3.

But you’re proving my point!

Best,

NS

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Hi, can you please tell me how many real numbers are between 1 and 2?

Hi, Just the Facts. It depends what you mean by “real.” Can you clarify?

Best,

NS

I hope I’m not repeating someone else but 1 is the loneliest number, not zero. Although it is possible to have nothing in your hand.

Dear Clay,

How can you object to the potter?

Please let me know,

NS