So if we can find a nice bijection between the real numbers the infinite sequences of natural numbers we are about done. Now, we know that $\mathbb{N^N}$ can be identified with the …

I am having problems being able to formally demonstrate when a function is bijective (and therefore, surjective and injective).

Composition of two functions - Bijection. Ask Question Asked 8 years, 1 month ago. Modified 1 month ago.

Jan 11, 2018 · A bijection is a function where each element of Y is mapped to from exactly one element of X. It should be clear that "bijection" is just another word for an injection which is …

Oct 24, 2010 · Step Two: We showed there exists a bijection between $\mathbb{N}$ and $\mathbb{Q}^{+}$. We now attempt to show there exists an explicit bijection between …

Apr 15, 2020 · A bijection is an isomorphism in the category of Sets. When the word "isomorphism" is used, it is always referred to the category you are working in. I will list some …

Having the bijection between $(0,1)$ and $(0,1)^2$, we can apply one of the other answers to create a bijection with $\mathbb{R}^2$. The argument easily generalizes to $\mathbb{R}^n$. …

Oct 9, 2019 · we can find a bijection between any two countable sets (I think this is correct) No. For example, some countable sets are countably infinite while others are finite. However, there …

Jul 14, 2015 · There is a bijection between $\mathbb R^4$ and $\mathbb R^3$, but no such bijection is linear, or even continuous. (Space-filling curves, which are continuous functions …

Show there exists a bijection between ideals containing $\ker(f)$ and ideals of $\text{im}(f)$ 1 Is there a bijection between the set of prime ideals of norm $~ q~$, and the set of ring maps to …