What is the next number after 38?

Answer 1

There is no NEXT number.

Suppose x was the next number.

That means 38 is less than x and there is no number between 38 and x (otherwise x would not be next.

Well, what about (38+x)/2?

It is easy to show that this is bigger than 38 and smaller than x so is between the two.

There goes the supposition that x was the next number.

So what about (38+x)/2?

The number halfway between 38 and this one will be better.

And the number halfway between 38 and the next one will be better,

etc,

etc,

etc.