3 ms·

Thanks I'm pretty sure somebody had taken the time. Here's another one for you. Could some uncountable infinities be cardinally smaller than countable infinite

Thanks I'm pretty sure somebody had taken the time. Here's another one for you. Could some uncountable infinities be cardinally smaller than countable infinites if we throw out the property that they must be countable by definition? As in you can say "this is smaller than that, I can demonstrate it's infinite but I can't do a countable demonstration."

lmm 4y ago
> Could some uncountable infinities be cardinally smaller than countable infinites if we throw out the property that they must be countable by definition? As in you can say "this is smaller than that, I can demonstrate it's infinite but I can't do a countable demonstration." No, trivially. If X has a smaller cardinality than Y then there is an injective function from X to Y (by definition), if Y is countable then there is an injective function from Y to the natural numbers (by definition), then by composing those two functions you have an injective function from X to the natural numbers i.e. X is countable.
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