Some math doodling, does this make logical sense?

Question

1/3 + 1/3 + 1/3 = 1

1/3 = 0.3~

0.3~ + 0.3~ + 0.3~ = 0.9~

That's to prove 1 = 0.9~, but... are we sure 1/3 = 0.3~?

x = 0.3~

10 x = 3.3~

10 x - x = 3.3~ - 0.3~

9x = 3

x = 1/3

Alright, the above calculations are a pretty old trick; but one day I was bored so I tried to expand this idea to something bigger.

The idea if x = x, then x - x = 0.

So if 1 = 0.9~, then 1 - 0.9~ = 0

Which means 0 = 1.0x10^-infinity.

So if you divide something by 0, there's two possible answers. Does Not Exist and #.0*10^infinity = infinity.

So if you divide something by zero, it equals infinity.

Answer 1

I'm not sure exactly what you are trying to get at here...

Answer 2

No. Dividing by 0 is not infinity. It is UNDEFINED.

Consider what you are asking when you divide by zero. You are asking -- "how many nothings are there in something," and presume that there must be some answer, perhaps "really really big." . But there simply isn't an answer --  it's a nonsensical question.

Nor is infinity the "really really big" number. Infinity is not a number of any kind. It is a concept that essentially means without bounds, or beyond conception.

Answer 3

And following the same logic with 0.9~ - 1 = 0,

0 = -1.0x10^-infinity, which would show that -infinity = infinity, which would in turn show that

0 = 1.0x10^-infinity = 1.0x10^infinity = infinity.

Just thought you'd like to know what your calculations imply.

Personally, I stand with most mathematicians in the belief that trying to do normal arithmetic with infinity isn't valid.

Edit@Blah: I appreciate the response to the negation, but to say that "infinity is not a number in any sense" is quite wrong.  It's true that it's not a real number, nor a complex number, nor admissible in any nontrivial integral domain (which is why most elementary algebraic techniques don't work); however, you seem to be putting this concept of a "number" (whatever they are) on a pedestal.  Numbers themselves are mere concepts, so why not admit infinity to be one too?

Answer 4

yes.