Does 0=1? (Math proof I randomly found)

So I was just messing around with some numbers and I found something weird.


0=0+0+0+0+0+0+0..........(goes on forever)


0=1-1

Right?

so,

0=(1-1)+(1-1)+(1-1)...........(goes on forever)


Applying the associative law of addition we can do this:

0=1+(-1+1)+(-1+1)+(-1+1)..............… on forever)

so then if we take away the infinite (-1+1)'s because it equals zero we get:

0=1

Am a right? If I made a dumb math mistake dont call me out im just 15

It gets worse.

The associative law can't be applied to infinite series that are not absolutely convergent.

Watch: apply the associative law as (1+1+1+..... on forever). Result: +infinity (note that infinity is NOT a number !). Apply the associative law to -1 and get - infinity.

Now you have +infinity -infinity and you are tempted to say :" Oh, that is 0!".

NO, infinity is NOT a number and it does not obey the laws of arithmetic. The answer can be anything (it is undefined)

Be aware that infinity + infinity is not 2x infinity, it is just infinity => it does not obey the laws of arithmetic.

Dealing with infinities is tricky .....

Not really, because when you used the associative law, even though you have infinite (-1+1)'s, you accidentally forgot a (-1) that is not paired up all the way at the end, just like the 1 you have in the beginning. The first 1 and the last (-1) cancel each other out, so 0=0. To illustrate a little, I will recopy and add a little to you work. the numbers do go on forever, but I'm including the very last number in each infinite chain:

0=0+0+0+0+0+0+0..........0+0+0
0=1-1
0=(1-1)+(1-1)+(1-1)...........(1-1)+(1-…
0=1+(-1+1)+(-1+1)+(-1+1)............(-1… -1
Now, you can see that the first 1 and the last -1 cancel out. Therefore, 0=0.

But, that is a really cool observation and if you use this kind of thinking, then you could make a pretty good mathematician. Keep it up.