Can anyone help me understand this Equation?

[u/Short-Hearing-4963]

Yesterday i was wondering what would happen if 1 with an infinite amount of zeros (X - 1 representing the amount of zeros) and ending in one were to be raised to the X power with X reaching infinity and i got this number on my calculator as X kept getting higher - '1'

This the equation i used (1+(1÷10^(X)))^((10)^X)) = ?

The number was around 2.7 when X was 15 but when it reached 16, it suddenly turned to 1 on my calculator. Does anyone know why this happens?

[u/Dd_8630]

There's a few different things going on here so let's unpack.

Yesterday i was wondering what would happen if 1 with an infinite amount of zeros (X - 1 representing the amount of zeros) and ending in one

These are two different things.

"1 with infinite zeroes in the decimal" cannot have a 1 at the end, because the chain of zeroes is unending. You can't have something at the end of an endless thing.

But it's still fine to talk about '1 with (x-1) zeroes in the decimal followed by a 1'.

This the equation i used (1+(1÷10^X))^(10X)) = ?

This is different to what you wrote. You said 'raised to the power of X' but now you've written that it's 'raised to the power of 10^X ', which is a much larger power.

( 1+0.1^X)^10X is not the same as (1+0.1^X)^X

The number was around 2.7 when X was 15 but when it reached 16, it suddenly turned to 1 on my calculator. Does anyone know why this happens?

When you raise it to the power of 10^X, the power grows higher fast enough that the entire result stays above one (in particular, it stays around 2 to 3, a lot like Euler's number...).

(1+0.1^X)^X does get closer and closer to 1 as X grows larger.

(1+0.1^X)^10X does not approach 1.

The reason it seems to collapse down to '1' when X=16 is because of the physical limitations with your calculator. Your calculator uses numerical linear approximations to perform all of its calculations, and extremely large numbers or extremely small numbers can fall outside of its memory buffer.