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## Is our math wrong? Is it our assumption of zero, or absolute nothingness?

There are know phenomena out there such as the gamma ray burst that total destroys(use loosely your ego wants to argue this syntax error not the mind) our current math and physics(e=mc2). But instead of saying well maybe we got a key part of our math wrong we make it so the phenomena matches our math. This is my personal take on what I think might be wrong. I think it has to do with our assumption of zero. Seeing how you can never have absolute nothingness as a base or starting point. Conceptually the idea of zero is great. I want an apple. But i am in a complete void of apples. I don't have a single one. Not even applesauce! I have ZERO apples. But I do not need to know that you have zero apples to know when you have 1 apple. On the other had I do need to know that you have 1 apple to understand that now you have 2 apple. I could be wrong. It just something that bothers me.

Also I am not a math person it has always been something I struggled with in school those pesky numbers. However in College I excelled at Logic, but that has been some time ago.

I am not say this is the answer I just say that I think there is something fundamentally wrong with our math

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## John Smith 30+

## Casey Christofaris 10+

Here might be a helpful video for you to understand that the world you call reality is just as imagined as the dreams you have at night.

http://www.ted.com/talks/lang/en/john_lloyd_an_animated_tour_of_the_invisible.html

## Jon Ho

To begin with, how do we define division? The ratio r of two numbers a and b:

r=a/b

is that number r that satisfies

a=r*b.

Well, if b=0, i.e., we are trying to divide by zero, we have to find a number r such that r*0=a. (1)

But r*0=0

for all numbers r, and so unless a=0 there is no solution of equation (1).

Now you could say that r=infinity satisfies (1). That's a common way of putting things, but what's infinity? It is not a number! Why not? Because if we treated it like a number we'd run into contradictions. Ask for example what we obtain when adding a number to infinity. The common perception is that infinity plus any number is still infinity. If that's so, then

infinity = infinity+1 = infinity + 2

which would imply that 1 equals 2 if infinity was a number. That in turn would imply that all integers are equal, for example, and our whole number system would collapse!

So, what now? How about 0/0?

I said above that we can't solve the equation (1) unless a=0. So, in that case, what does it mean to divide by zero? Again, we run into contradictions if we attempt to assign any number to 0/0. Let's call the result of 0/0, z, if it made sense. z would have to satisfy:

z*0=0. (2)

That's OK as far as it goes, any number z satisfies that equation. But it means that the result of 0/0 could be anything. We could argue that it's 1, or 2, and again we have a contradiction since 1 does not equal 2.

## Jon Ho

But perhaps there is a number z satisfying (2) that's somehow special and we just have not identified it? So here is a slightly more subtle approach. Division is a continuous process. Suppose b and c are both non-zero. Then, in a sense that can be made precise. the ratios a/b and a/c will be close if b and c are close. A similar statement applies to the numerator of a ratio (except that it may be zero.)

So now assume that 0/0 has some meaningful numerical value (whatever it may be - we don't know yet), and consider a situation where both a and b in the ratio a/b become smaller and smaller. As they do the ratio should become closer and closer to the unknown value of 0/0.

There are many ways in which we can choose a and b and let them become smaller. For example, suppose that a=b throughout the process. For example, we might pick

a=b = 1, 1/2, 1/3, 1/4, ....

Since

a=b,

for all choices of a we get the ratio 1 every time! This suggests that 0/0 should equal 1. But we could just as well pick

b = 1, 1/2, 1/3, 1/4, ....

and let a be twice as large as b. Then the ratio is always 2! So 0/0 should equal 2. But we just said it should equal 1! In fact, by letting a be r times as large as b we could get any ratio r we please!

So again we run into contradictions, and therefore we are compelled to

let 0/0 be undefined.

So, yeah, zero does not exist, unless if you studied calculus and learn about Rule of L'Hôpital. Which then gets pretty whacky and my hands are all tired from typing and steering this spaceship at the same time so I am ashamed to tell you to just Wikipedia it. Sorry.

## Casey Christofaris 10+

## John Frum 30+

Incidentally, how many digits are there in the decimal expansion of √2 ?

## Jon Ho