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0/0

Question

When I was like 5 my dad told me you can't divide 0 by 0. I set out to prove him wrong...

1) N represents every and any single number

2) A*B = C can be rewritten as C/B = A

Example: 5 * 2 = 10 is the same as 10 / 2 = 5

3) A rewrite of the A*B=C:

N*B = C

C/B = N

4) Substitute C and B for 0:

N*0 = 0 (this is correct, think of 5*0 = 0 or 100*0 = 0, N=anything, anything times 0 is 0, so N*0 = 0)

0/0 = N

The logic is undeniable. 0/0 equals any possible number, and every possible number. Even 0. Using reverse multiplication or whatever its called.

BUT then a couple days ago I realized that its possible for the entire base of the logic to be shifted...

yes NB = C can be rewritten as C/B = N

but to do so, don't you use algebra:

NB = C

/B /B (divide by B on both sides)

N = C/B

remember B and C are both 0... so dividing by B is dividing by 0. So yeah once again 0/0 evades the only solution possible.

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the reason that works is because 0/0 has no answer

it is undefined

it isn't zero it isn't 1 it isn't 2

it isn't anything, but when you represent N as anything it also becomes everthing, wich is realy no single thing.

so yes 0/0 can be anything, but it can be no single thing, it has an infinite number of possibilities

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exactly. N is an infinite number of things. any number. every number. we're talking all positive numbers, all negative numbers, 0, all fractions, all endlessly repeating or endlessly crazy decimal numbers (like pi). Or even imaginary numbers (i).

and N*0 = 0

so 0/0 = N

you can replace N with any number you want

but even that can be questioned, if you question the rule that is based on...

sure 5*2=10 can also be expressed by 10/2=5, but do you have to use algebra to make the switch?

5 * 2 = 10

divide by 2 on both sides

5 = 10 / 2

or can you just automatically make the switch?

thats the question. if you can, 0/0=N. If you cant, my equation equals out to: 0/0=0/0

lol

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this is why we have limits in calc and L'Hopital's rule for equations, and if-then statements in programming. Some guy was so bold to call 0/0 'nullity'.

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hehe... nullity

what's L'Hopital's rule?

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it's calc dude don't worry about it

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