Why ℕ ~ {2x|x∈ℕ}?
I actually understand this but I can’t explain this to my father who says that ‘for each even natural number there are 2 natural numbers’ – How can I explain this concept to him in a way that he will understand? (not saying he is stupid or anything he just cant figure it out)
In: Mathematics
>”For every even natural number there are 2 natural numbers”
Really? Because I can pair every natural number with an even natural number, and there will be no number left over in either set.
0 => 0
1 => 2
2 => 4
3 => 6
4 => 8
5 => 10
and so on.
We say two sets have the same cardinality if, for each element in one set, we can find a matching element in the other set with no numbers left over.
Ask your father what natural number is left over once all the even natural numbers have been assigned a partner.
Or, if you want to really do his head in, explain that while natural numbers and even natural numbers are the same cardinality, real numbers and natural numbers don’t. There are infinity more real numbers than natural numbers.
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