**UPDATE:** Please read all the comments before commenting on how stupid this is. Thank you.

I’ll preface this discussion by stating straightforward that my knowledge of mathematics is rudimentary at best, and my “expertise” lies in the most basic algebra. That said, I’ve concluded that fundamental math is flawed. This observation renders the teaching of math in any educational institution completely unnecessary, and, in addition, changes the manner in which man views his world. Allow me to propose my argument.

Take a standard polynomial equation, ax^{2} + bx + c = 0. For the sake of clarity, we’ll plug in some arbitrary numbers – x^{2} + 5x + 6 = 0.

Since we know the entire equation equals zero, we can freely add the equation to itself on either side as many times as we like, since we’re adding nothing. Adding it to the right side, we get x^{2} + 5x + 6 = 0 + x^{2} + 5x + 6.

Since it’s just adding zero, we might as well do it again. Let’s again add the equation (which equals zero) the right side. That gives us x^{2} + 5x + 6 = 0 + x^{2} + 5x + 6 + x^{2} + 5x + 6, or x^{2} + 5x + 6 = 0 + 2(x^{2} + 5x + 6). We might as well go ahead and take out that zero since it doesn’t matter, so that leaves us with x^{2} + 5x + 6 = 2(x^{2} + 5x + 6).

Suddenly, we see that the left side is equal to itself times two. The equation can be written like this: 1(x^{2} + 5x + 6) = 2(x^{2} + 5x + 6), and we see that the areas in parenthesis are the same, so we can divide those out, leaving us with **1 = 2**.

**Oh, but wait.** Here’s a problem, you say? What we are dividing out is equal to zero, and therefore cannot be placed in the denominator? This is not only incorrect, but fundamentally absurd. The problem lies in the very basic principles of mathematics. In dividing zero by zero, we are not left with something which is undefined. In actuality, it is quite definable – it is infinity. Division is the act of dividing a number, and just as ten may be divided by five to yield two, nothing (zero) is divided by nothing to yield infinity, since nothing can be placed into nothing infinite times. Five two times is ten, just as zero infinite times is still zero. Furthermore, *any *number divided by zero is not undefined, but instead equals infinity, since nothing may be placed into any amount an infinite amount of times.

Math, at its crudest level, expects the user to concede that it is impossible to define zero placed into zero, and it is on this assumption that all else is based. If we fail to accept this clear fallacy, we fail to accept math. We can add x^{2} + 5x + 6 even more times to our equation, dividing it out, in order to make 1 = 3, 2 = 4, etc. No longer is any number assigned its own value – everything is equal. Math explodes.

I’m going to make a comment because I know you guys who know a lot more math than I do are going to rip me apart. CONSTRUCTIVE CRITICISM, please. I know it’s possible to prove this – help me out.

Do you really think anyone is going to read this whole thing? Well…maybe some people will…Anyway, I’m going to go ahead and say “You’re right! Way to go!”. Now come see me.

Peace!

L.

Some people might have some good insight on this subject.

Yeah I’m not reading it. bf tomorrow.

I read it.

WAR!

W.

War?

You are flawed in your logic, because while we define a number divided by 0 as infinity; infinity itself is undefined. The basis of all math is addition. And no numbers than can be derived from 1 added to itself or added in any concrete manner can ever actually reach infinity. If you are trying to disprove math using a formula, break it down the simplest parts, and you will see that in the shorthand representations complications can occur. (e.g. x^2 + 5x + 6 is really x added to itself x times plus 5 more x’s, and then an extra constant 6.) so let’s actually give x a value, and since (-2 and -3 are the answers to the problem, we will use -2). broken down into parts, you get x^2 = -(-2 + -2), 5x = -2 + -2 + -2 + -2 + -2, and 6 all added together. and after elementary school, we all know that 4 – 10 + 6 = 0. after algebra we get the rules that tell us that 4 – 10 + 6 = 4 – 10 + 6. we also learn that adding zero to either side will leave us with the same answer. so if you wanted to add some random numbers to one side of the equation in attempt to overly complicate things, we come to 4 – 10 + 6 = 4 – 10 + 6 + 4 – 10 + 6. and we simplify to 4 – 10 + 6 = 2(4 – 10 + 6), but seeing as how you can multiply throught, you get 4 – 10 + 6 = 8 – 20 + 12. And these numbers are irrevokably equal.

I believe the thing that you are disproving is not math itself, but the inadequacy of algebra to describe itself in full detail.

ps walt is playing battlefield

You CAN multiply through once you reach 4 – 10 + 6 = 2(4 – 10 + 6), but you don’t have to – you could instead divide each side by 4 – 10 + 6 (the equivalent of what I did), yielding 1 = 2. But you’d have to divide by zero, which is why I tried to justify doing so.

I don’t quite follow what you’re saying about infinity. I understand that it would be impossible to ever “reach” infinity, but I fail to see why you couldn’t divide out the sides and end up with what I got, unless you’re implying that one side would be infinity (in which case I still think it’s cool that you could make any number equal infinity). Please clarify.

I found this site. The part that most interested me was this:

That makes it sound like it’s only out of convenience that we can’t say that all numbers are equal.

Okay…this is simple.

You actually never divide by zero. You can claim it’s zero because it can be simplified into zero, but “4 – 10 + 6” is not zero.

If you claim it’s zero, you’d have to simplify it into zero, so it becomes 1(0) = 2(0), which is actually 0 = 0.

But unsimplified, that equation has value…which means you cannot just add it to one side without the other, even if the end result is zero.

Also, I’m pretty sure you can’t place nothing into nothing infinte times. You have nothing to place.

You cannot place something you don’t have…and you sure can’t place the thing you don’t have into something that’s not there as many times as possible.

infinity isnt a number, its an idea (think of it as a variable).

to say that a number divided by zero is to say that zero times infinity is THAT number.

it is common belief that infinity is infinity is infinity, when in all reality, there are varying degrees of infinity.

take the lines f(x) = x and g(x) = 2x.

when y is sufficiently large enough to be deemed infinity, the first line will be at the same proportion of infinity while the second the second line will be at infinity also, but the second line will be twice the height of the first line.

Infinity is measured in rates. therefore, you could say that 2/0 = 1/0, and get that infinity = infinity. which is nominally correct, but the left side of that equation would have an infinity that grew twice as fast as the infinity on the right side..

make sense a little more?

hmmm. the thing that i like about this the most is that it is very similar… perhaps IDENTICAL to something that was developed by andrew, tim, daniel, trey, and scott (listed in alphabetical order by surname) during our junior? maybe senior year.

yet here it is set forth as something completely developed by yourself.

way to be a fucking asshole, scott.

okay, last comment was a knee-jerk reaction, but everything i said in it still stands.

now, however, i have actually read through the post/comments in their entirety.

okay, first of all, from my point of view, you left out a very important point in the original post, scott. that is this: when you divide a given number by a relatively large number, you get a small number. (10/100 = 0.1) when you divide a given number by a relatively small number, you get a large number. (10/0.1 = 100) it logically follows, therefore, than when dividing by a number with no quantity will give you a figure of infinite quantity. (10/0 = infinity) however, im sure even this line of thinking is flawed (in part because of the fact that division doesn’t really exist, it’s just another way of describing multiplication)… but i’m not really sure. in any case, i think it’s one of the simpler ways to support what youre saying.

i, however, no longer support the postulate you present in the opening article.

here is why… it’s not a fancy-schmancy mathematical proof, it just lies in the analysis of mathematical theory…

basically, math is a set of rules that, when followed, always yield certain set of solutions. it operates on a number of (sometimes really obvious) assumptions, such as when we write “1” it represents a sort of singular unit.

another of these assumptions is that we cannot divide by zero. there’s not point in assuming or trying to prove that we can divide by zero… it just isn’t possible, given that we follow the rules of math. it is true that IF we could divide by zero, math would break down. but math is a system that allows us to do many kinds of things, and theres no point to arbitrarily seek ways to make it fail.

i dont know if the point im trying to make is really coming across.

math is a set of rules that allows you to plug certain variables into certain operators and get a consistent, predictable, reproducable set of results. furthermore, it is a system that allows us to do a variety of things which would otherwise be impossible or very complicated. one of these rules is that you cannot divide by zero. if you dont follow this rule, the system breaks down. however, the system works and is an incredible tool. so there is no point in arbitrarily breaking the rules in an attempt to disprove it.

sorry if there are a lot of typing errors or misspellings; i’m on my mom’s laptop and it’s hella hard to tell wtf is going on.

finally: yeah, go see lauren! im sure she’s lonely here in boring old shreveport now that the majority of her boyfriends/fuck buddies are a coupla hundred miles away.

*open high five so dont leave me hangin*

on a side note: walter, were you, in fact, another of the people who contributed to this?

if so, i am sorry for not mentioning you.

i, unlike some people, am concerned with giving credit where it is due.

OK, first of all, I’m pretty sure I was the one who came up with the polynomial thing, and I know that Walter and I asked some Asian dude in our computer science class about it, and he’s the one who emphasized the importance of not dividing by zero. That said, I know we all spent time thinking about it but I wasn’t trying to take credit away from any of y’all – I thought I was presenting what I had originally and that various people would come give their inputs in the comments, like so, in order to make it complete.

To Austin’s comment – I’m not really sure I understand your first comment, but your second one helps. I never looked at it from the other perspective, but I guess that logically you could either say that nothing could be placed into nothing infinite times or no times. I can see an argument for both.

Now, to Trey’s comment – yes, Mr. Evans did a good job of explaining how one could have various “degrees” of infinity, but your final conclusion that one side’s infinity grew faster than the other side’s infinity would still make something equal something it doesn’t, and still screw up math.

Daniel, your point about the division of large and small numbers is a good one and helps to further what I said. Breaking the rules of math was my point though – if one could prove that an original rule of math was unsound, there’d be no reason to adhere to the rest of them and the whole system would break down, as you said. You say there’s no point in trying to break the rules to disprove it – well then, you should be completely disregarding this entire concept, because you apparently have more respect for math than I have. ๐ And finally, what the hell should it matter to you if I see Lauren?

i dont know if i was part of that or not

i dont care

it’s drinkin time

hooray for alcohol

Okay…a second go at this…

ORDER OF OPERATIONS!

You have to do what’s in the () before you can do anything else.

Well even if you reduce the parentheses, at that point I’d just say divide out the zeros and stick with 1 = 2. ๐

first of all, i wouldn’t say you’re proving an original rule of math to be unsound. i would say it’s more like your exploiting an apparent indiscrepancy that, upon further inspection, is actually not a discrepancy at all (given, of course, that you follow the OTHER rules within the system).

i dont really have a second of all; i do, however, have other things to say.

it’s not really a respect for math that i have… although, i guess i do. i dont understand if youre not getting the point im trying to make, or if im not getting that youre getting the point im trying to make.

math is a system that, given one follows the rules, works. if you break the rules… naturally it won’t work.

take baseball, for instance. baseball is a game that produces… well, supposedly, “entertainment.” whatever. okay, let’s pretend like you arbitrarily make it so that players are no longer able to be “out.” caught balls, three strikes; whatever, no “outs.” suddenly, the game breaks down. it never progresses past the first half of the first inning, because whichever team is at bat just makes runs indefinitely.

mathematics is a system with rules. follow the proper rules, get the proper result. break the rules, and, by definition, the result will be mathematically unsound.

hmmm. i get the feeling that i am just repeating myself. if i am, apologies… im just trying to clarify something that im finding difficult to properly explain.

finally, this. scott, despite our differences, i consider you a friend. now, all i ever hear about lauren sadasivan is how she hurts other people’s feelings. seriously. the only times i hear about her anymore is when she has hurt somebody else/again. therefore, as someone who considers you a friend, i feel it is my duty to steer you clear of such negative people. but i’m not your mom; whatever you want to do is up to you. i just seriously dislike people who consistently hurt the feelings of those i care about.

I understand what you’re saying, but my whole point was to break the rules of the system in order to break it down. That’s all I’m trying to do. You may see it as pointless – but hey, I was bored.

I appreciate your concern, but there’s always more to the situation than someone on the outside can infer.

It doesn’t work because while x/0=00 (00=infinity kinda brute infinity symbol) what you really need is lim(x) as x->0 which is undefined thus dividing by 0 is undefined. Also there are flaws in algebra in general and some errors in yours, which is why we use Calculus to really explain all this.

Max!!!

Bringin’ in some closure!

Thanks a lot, man.

Truly, great insight. I only wish I still had the slightest academic need for math.

YOUR maths severely flawed.

ax2 + bx + c = 0 —– (1)

substituting each variable, a b and c with integer,

x2 + 5x + 6 = 0 ——– (1)

because x2 + 5x + 6 = 0, we can safely add x2 + 5x + 6 on the RHS.

x2 + 5x + 6 = x2 + 5x + 6 ——–(2)

now i don’t understand what logic is that you claim, and i quote:

“we can freely add the equation to itself on either side as many times as we like, since weโre adding nothing”

after equation (2), anything added, multiplied,subtracted, divided on the LHS has to be applied to the RHS as well else you’re contradicting to the laws of equality.

If you can’t even understand the basics in algebra and yet has the audacity to put up a post like this, ptffff…… you’re no smarter than my famicom.

I appreciate your use of tact, avoiding personal attacks over something so controversial as an opinion on mathematics. And you wouldn’t believe my audacity, I assure you.

My whole point was that there are these (possibly) flawed “laws” which must be followed in order not to break math. You say, “after equation (2), anything added, multiplied, subtracted, divided on the LHS has to be applied to the RHS as well else youโre contradicting to the laws of equality.” Simply adding something that is equal to zero to one side of the equation and not adding it to the other side shouldn’t mess anything up – after all, it’s ZERO, NOTHING. 7=7, and 7+0=7 (you don’t need to write “7+0=7+0”).

But then it all goes back to the “dividing by zero” thing, which you must say is impossible (but I disagree). Max was right about that.

Thanks for stopping by.

Also, I was clearly exaggerating/being sarcastic when I said things like “this will change the world” or “disprove math,” or that I have any expertise at all. I don’t really care much about this post or its concepts anymore. ๐

One can have an opinion about anything…even something as “irrefutable” as math.

This is purely theoretical crap anyway, and the theoretical will always be subjected to peoples’ opinions. And it’s thinking like yours that will keep the perpetual motion machine from ever being built.

You think I haven’t devoted all my life to the PMM? What do you think all my comics are about? They’re actually schematics! Don’t give me lip about not believing in the PMM…

Watch the Axminster video:

http://cghm.org/wow/2009/damn-you-axminster

http://www.math.toronto.edu/mathnet/falseProofs/fallacies.html

no further comments.

0/0 has no one definition.

In calculus, a number divided by zero has similar properties to both infinity and negative infinity in many cases

0/0 can be anything

just because the equation is equal to zero doesnt mean you can skip adding to the left side; this is why we have the addition property of equality.

scwtte, let me just say that the poster under pseudonym “fibonacci numbers” above is wrong.

If x2 + 5x + 6 = 0, you can indeed add x2 + 5x + 6 to either side, any number of times and still keep a valid equation, only with some additional constraint in the need to be on guard for division by zero.

As for division by zero itself. I’ll try to explain things the way I see them. While many will refer to mathematics as pure, universal logic, it both is, and is not. In the end mathematics is a system, as defined by us, and we define it as not to cause logical contradiction. As such, we define 0/0 as undefined, as silly as that sounds. It’s a choice, not one made without reason, there are many, but a choice none the less, a decision made to avoid contradiction.

These choices, our definition and our axioms seem to originate from our intuition, maybe not in modern mathematics but in the ancient roots of counting, it’s in us with even infants showing recognition at the concept of numbers. What I am trying to say is that throughout much of our history mathematics has been both a tool and something worthy or study in its own right, and it is both, but our axioms and definitions are chosen by us, for these purposes, and we can choose a different set thereof to form a different tool for a different task, or to study logic and mathematics in a different way.

It is perhaps improper to speak of “mathematics” as a singular entity but rather to view it as a collection of logical constructs, multiple mathematics.

As I am about to post this I note the date on both the original post and the latest of the comments before mine own, still, links to this is in circulation and to any later poster I hope I bring some clarity.

M. LeBlanc,

Let me just say thank you for stopping by and taking the time to comment. I still enjoy seeing what (positive) thoughts people have to share about this topic.

(And I’m not a bot, although this sounds like an automated reply.)

In fact inadvertedly you are proving that 0/0 is undefined.

What you are doing is imposing that 0/0=1, and you are arriving to an absurdity 1=2. But if instead of imposing that the zeroes cancel each other you look at what the equation is telling you, you’ll see it tells you 0/0=1/2. But also 0/0=2/1. And as you say you could achieve any value for 0/0. Therefore it makes sense to say its undefined, and we remove all absurdities.

Secondly, you are wrong in saying that any number other than zero divided by zero equals infinity. It is also undefined. From the positive side, it aproaches infinity. From the negative side, minus infinity. Therefore something over exactly zero is undefined.