Question

Give an example of an infinite set.

Answer 1

Are the the numbers you count with infinite?

Answer 2

Think about integers, or real numbers.

Answer 3

Yeah I think so

Answer 4

Yes exactly, so the set of integers is an infinite set

Answer 5

So like what? Could {1,2,3} be an infinite set?

Answer 6

No, an infinite set is a set with an infinite number of elements. \(\{1, 2, 3\}\) has 3 elements, so its finite.

Answer 7

so I wouldn't be able to give an example?

Answer 8

So consider the set of integers. Is there a finite number of them? No if there was there would be a largest integer but there isn't a largest integer.

Answer 9

Do you see why the set of all integers is infinite?

Answer 10

No, this is just furthering my confusion

Answer 11

Consider this set \(\{..., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 ....\}\)
with no smallest or largest element, it goes on forever.

Answer 12

This is the set of integers.

Answer 13

soo would something like {1,2,3...} be like an infinite set?

Answer 14

The ... just signifies that it goes on forever in the same pattern. So what you are really saying is
1, 2, 3, 4, 5, 6, 7, 8, 9, 10 .... going on forever

Answer 15

\(\{1, 2, 3, ...\}\) is just the positive integers

Answer 16

This is just making more confused