Does infinity necessarily need to include ALL real numbers?

Question

In other words, could you say that there is an infinite set of real numbers that are NOT a particular real number x – hence “infinity” does not necessarily need to contain all real numbers?

In: 3

Answer 1

0, 0.1, 0.01, 0.001, 0.0001, etc.

You can keep going on for forever, and you will always be bounded between 0 & 0.1.

0, 0.01, 0.0001, 0.000001, 0.00000001, etc.

The above still goes on forever, but it skips 1 decimal place every time, so it’ll include every number from the first list, but only ~1/2 from the first list will appear in this list, yet both are infinite.