/sci/ - Science & Math

>>15043801
>Are only the zero mapping and identity mapping candidates for linear mappings?
Nah. Stuff like [math]x \to ax[/math] is also linear.
>>15044925
If the sum is always bounded above, then the [math]A_n[/math] aren't just countable, they're finite (there's a simple, explicit upper bound on [math]|A_n|[/math] which I'll let you calculate).
You then prove that, since all of the [math]A_n[/math] are finite, [math]A[/math] is countable.