From the years ago, it has always been this question in my mind which a teacher of high school talked about in a class but I never found it's correct answer.
We have set of natural numbers ${1,2,3,4,5,...}$ and set of real numbers.
We have two concepts to prove that these sets of numbers are equal or smaller than each other.
Concept 1
If we choose any number from the natural numbers, we can choose a number from real set of number, so they are equal.
Concept 2
Natural numbers are subset of the real numbers, so natural numbers set is smaller than set of real numbers.
Which concept is correct?
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