How many ways to make a thousand?

Answer 1

Infinitely many.

Start with the sum of two integers:

500+500, 499+501, 498+502 and so on for infintely many pairs.

Then consider number with one decimal places:

499.9+500.1, 499.8+500.2, 499.7+500.3 and so on.

Then consider numbers with two decimal places, three dp, four dp, and so on, up to infinitely many dp.

Next consider triplets of numbers, such as 333+333+334, 332+333+335, 331+333+336 and so on. Once again you can have numbers to 1 dp, 2 dp and so on.

Then you can have sets of four, five, six and so on.

And you have not even started on multiples, or quotients, or exponents.