It is defined that {0,2,4,6,8,...} and {0,1,3,5,7,...} and {0,1,2,3,4,5,6,7,8,...} are all the same size because they are all denumerable. (By whom it is defined, I don't know; I parrot your teaching here). If it matters to physics, then the definition is meaningful and useful, otherwise (and regardless of it's self consistency) it is just an arbitrary and useless invention of man's intelligence.
Can you give ONE real life example where it physically matters in the slightest whether some people think that the set {0,1,2,3,4,5,6,7,8,...} is twice as large as either the set {0,2,4,6,8,...} or the set {0,1,3,5,7,...} as opposed to the accepted er... wisdom that all three sets are equal in size?
I am hoping that you can. Otherwise you just wasted my time except for the mental excerise that I got. (not inconsequential, that)
---Al
