/sci/ - Science & Math

>>12311524
I'm not being combative.
For an extremely easy to check example, the vector space [math]\mathbb{Z}_2^{\mathbb{N}}[/math] has an uncountable number of elements, by the classical Cantor argument, but the countable infinite dimensional [math]\mathbb{Z}_2[/math] vector space, that is, the vector space of finitely supported maps from [math]\mathbb{N}[/math] to [math]\mathbb{Z}_2[/math], has a countable number of elements. What this implies is that the countable infinite dimensional vector space can't be written in the form [math]\mathbb{Z}_2^{X}[/math], independent of whatever [math]X[/math] you choose.

Do apuposters have actual mental problems?