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### Positive and negative infinity

We cannot really imagine what infinity is. This applies both to infinitely large (just think of the universe) and infinitely small. In mathematics you make a difference between positive infinity and negative infinity. That's even more incomprehensible.

*Is that just hocus pokus?*

##### Positive infinity

For calculating the number * e* we use the formula

and try to find the correct answer. We start with simple numbers

Eventually we find the correct answer. That is the transcendental number *e =* 2.7182….

##### Negative infinity

In the same way we solve the formula for *negative infinity*, and write

Once more we start with simple numbers. We begin with *n* = –1, and get

That is undefined. That doesn't help much. So we take *n* = –2, and see

That is better. Now we continue with *n* = –3, and find

That is a little less. So we take *n* = –4, to find out what happens next

The decrease continues. With *n* = –5, we get

With *n* = –6, we see

Now we take *n* = –10, and just write

A bigger step with *n* = –256 shows

With *n* = –1024 you see

That comes quite close to what we previously have calculated. So we try *n* = –4096 and get

This answer is correct to 3 decimals. So here it makes no difference whether we calculate with negative infinity or positive infinity.