>>19
Find n which satisfies 0!=0*10^n then
>>20
∞
>>21 Time to introduce some infinite cardinals.
The expression 0*(10^n) is equivalent to
0*(10*10*10*...) what it means to multiply by 10? 10*x=x+x+x+(10 times)
so the form of this series can converted to 0*(10+10+10+10+...)
what is value of n*(x+y+z)? (x*n)+(n*y)+(n*z);
the values of expression becomes ((10*0)+(10*0)+(10*0)+...)
simplified to 0+0+0+0... ,where each step of the series is compacted 0+0=0 to zero, giving exactly 0 at every step, resulting in 0.
>>22
Infinity is not a number, you can't treat it as such.
>>23
At which point the series 0+0+0+... results in non-zero result? At every step(0+0) the result is zero.
>>25
Try calculating it for an infinite number of terms by hand, I'll wait until you finish.
>>25
0+0+0+... is a series where each step adds 0(except initial)
0(+0)(+0)(+0)... combine with the property of zero, is that it doesn't alter the result of number, when its added x+0=x
With this we can conclude that each op(+0) doesn't alter the result of number before it. https://en.wikipedia.org/wiki/Additive_identity
Since the series consists of NOPs which don't alter results of previous computation and don't add extra computation with more steps, the only significant number is the initial 0.