If 0 is smaller than 1/Infinity, does that mean that 1/0 is bigger than Infinity?

Well, The Absolute Value of (1/0) is Infinity.

I belive that "1/∞ = 0" because lim x→∞ [ 1/x ] = 0

However 1/0 is undefined and the following is a prove by using limit.

lim x→0+ [ 1/x ] = ∞

lim x→0- [ 1/x ] = -∞

0 is equal to 1/infinity

1/0 is undefined. People say it's infinity, but that would mean 1/-0=-1/0=-infinity, which is way too many values. So... not really? Infinity is a strange concept.

Yes I have dwelt on what you are saying.

(1/0)=-(1/0)

For it is true that, (1/0)+(1/0)=(0+0)/(0*0)

Which also equals (1/0)+(-1/0) which equals (1*0)+(-1*0)/(0/0)

yeah.

Kinda. Dividing 0 is weird. Really weird.

FALSE PROOF:

0*1=0 (divide 0 on both sides) 1=0/0

0*2=0 (divide 0 on both sides) 2=0/0

1=0/0=2 so 1=2

Yes 1=0/0,

as does 2.

If x^0=x/x, then at 0, x^0 shall equal 0/0.

x/x=x^0=1

0/0=0^0=1

but...

0/x=0^x=0

so 0/0=0^0=0

another strange question: ARE THERE AN ODD OR EVEN NUMBER OF INTEGERS?

There are half as many and at the same time the same amount of even numbers as naturals.

See how they can be lined up.

1-2, 2-4, 3-6, n- (2n-1)

Yes exactly as many this time.

There are as many 2n's as (2n-1).

here's another way you can think of it:

pair numbers up that add to 0. 0 is then by itself, so there are an odd number of integers.

pair numbers up that add to 1. 0~1, -1~2, -2~3... -infinity~infinity (remember infinity+1=infinity) and nobody is left out so there are an even number of integers.