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
A good metric to look at is if a set has at least as many elements as another set. This can be checked, so that A has at least as many elements as B if you can pair their elements up and still have some leftover in A but not in B. Your dad will probably agree to this.
So, let’s say A=ℕ and B={2x|x∈ℕ} (so I can write it down more easily). If we pair every n in B up with the same number in A, then we have leftover in A but not in B, so A has at least as many elements as B. If we pair every n in A up with 4*n in B, then we’ll have leftover in B but not in A, so B has at least as many elements as A.
As both sets have at least as many elements as the other, it follows that they’re equal. If your dad still disagrees, ask him which step of this progress is supposedly incorrect.
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