system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: What is Euler's Number supposed to mean/represent in math?
gpt
Imagine you go to a bank that has 100% interest on your savings account. They double your money deposited every year. That's great! You start with $1, and at the end of the year have $2.

But then another bank has a better deal. They give you the same 100% interest, but they give it to you in two chunks. So at the 6 month mark, they give you 50% interest ($1.50 total), and then at the one year mark, they give you 50% interest on your new total, so you end up with $2.25.

Not to be outdone, the first bank now divides their interest monthly. Each month you get (100/12)% interest. At the end of the year, you end up with $2.61.

Now another bank comes back and offers interest daily. Each day you get 1/365th of your interest, so you end the year with $2.71.

Now let's take it to the extreme and compound it every minute. 525,600 minutes in a year (Thanks Rent). We find that at the end of the year this way, we end up with... $2.71. There's some changes in the decimal value after the fact, but we've pretty much reached our peak.

The equation we would use for calculating our interest was (1 + 1/N)^(N), where N is the compounding period. As we make N bigger, the exponential value gets larger, but the fraction gets smaller. If we make N infinite, that's when we get Euler's Number (e) out of this equation.