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Division by zero
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Why cannot divide by zero? Tell me /Sci/ mathematical dumbos.
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>>7845901
You can't divide by real numbers since they don't actually exist
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>>7845901
Back to >>>/r/eddit
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consider the function 1/x for any real x. as you get really close to 0 from either side, the output of the function gets bigger and bigger.

what should the output be when x = 0? it must be bigger than all the other outputs, which cover all real numbers. so the function must be infinite there. But infinity is not a real number, so 1/0 is undefined.
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>>7845901
4/0 = 0 = 5/0
4/0 = 5/0
(4/0)*0 = 5
5 = 0
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>>7845913
What about the largest "cantor infinity" possible?
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>>7845917
Who said 5/0=0?
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>>7845901
It's excluded axiomatically.

https://en.wikipedia.org/wiki/Field_(mathematics)#Definition_and_illustration

Ignoring that, you could show that if you allowed division by 0 (while maintaining other all other properties of division) you can reach a contradiction.
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>>7845922
Seems like some idiot mathematician excluded it and every other mathematician followed.
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>>7845920
You can follow the same logic for why 4/0 = 0.

You have 5 apples and keep them yourself and eat them so there are no apples left.
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>>7845931
Apples are made of energy, and energy cannot be created or destroyed.
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The way I've always thought of it is that 0 is not a number in the same sense that 1, 2, sqrt(2), pi, e, etc... are numbers. 0 is an absence of a number. It's like an empty position. It's a null value. So dividing by it simply doesn't make any sense since it doesn't have the same properties as every other number.
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>>7845955
0 is the set of the empty set. Which, us not the absense of a set. Dumbass.
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>>7845964
*is
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>>7845926
Did you read the second part of my post?

Suppose that we can divide by 0 but we leave all the usual rules intact then, further suppose that $a,b > 0$ then $\frac {a} {0} = b \implies \frac {a0} {0} = a = b0 = 0$ so we reach the conclusion $a = 0$. But a is greater than 0 by hypothesis, thus we have a contradiction. $\blacksquare$

We could go on and show more contradictions, but I'm not going to do that one is enough.
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>>7845901
if you divide by something approaching zero, you get somthing that approaches infinity.
But dividing by a zero makes quite a problem, because uh... it's certainly not infinity, because the reverse operation does not yield zero...
So it's "undefined" then
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>>7845926
If you chose to include division by zero, you get a different algebraic structure that is not a Field, like Complex or Reals.

It's not that you can't, its just that if you chose to include then you get all new properties.

Not that explaining that to you will accomplish any good. You seem intent on being uneducated.
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>>7845901
$0^{+}=0$
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>>7848057
You bumped this thread, from the last page, to post that? I fucking hate faggots like you.
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>>7845913
Not true, as you approach 0 from left side results get smaller and smaller

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