May 16, 2015 · Bijective means both injective and surjective. This means that there is an inverse, in the widest sense of the word (there is a function that "takes you back"). The inverse is so …

But I think there is another, faster way with rank? I hope you can explain with this example? For square matrices, you have both properties at once (or neither). If it has full rank, the matrix is …

Jan 6, 2024 · Condition 3 is necessary, but not sufficient: a linear map between two spaces of different dimensions cannot be bijective. Since often one knows the dimensions ahead of time, …

Hint: Can you map both of sets bijectively to $\mathbb {N}$, then compose the maps to give a bijection between the two sets?

Nov 27, 2016 · Anyway, my question is on how to show that the complement operation (viewed as a function from the power set of a set S to the power set of S) is bijective. Some suggested …

Nov 21, 2020 · What exactly is the domain you're considering? (I can probably guess, but you really ought to be specific about these things.) As for showing that it's bijective, a drawing is …

2 A function is injective if and only if it has an inverse if and only if bijective onto its image.

Prove that if $E$ is compact and $f$ is bijective then $f^ {-1}:E' \to E$ is continuous. I know one way to prove it is by showing that if $S\subset E$ and $S$ is closed then $f (s)\subset E'$ is …

Both of these mappings are injective, so we can use the proof technique to build a bijective mapping $h$ between $A$ and $B$. The number $1 \in B = (0,1]$ is a B-stopper; let

Nov 20, 2016 · 4 This function proves N N has the same cardinality as Z Z. But as for your question, the function is bijective because it is injective and surjective, both of which are easy …