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 1d comment If $A,B$ are sets and $B$ is finite, and there is an injection $f:A \to B$, then $A$ is finite and $card(A) \leq card(B)$ Yeah, you'll need to prove that a subset of a finite set is finite. Here's a good proof: proofwiki.org/wiki/Subset_of_Finite_Set_is_Finite May 3 comment Assuming that the sum of the angles of any triangle is 180, how can I deduce Euclid's 5th postulate? Please explain downvote May 2 comment If $A,B$ are sets and $B$ is finite, and there is an injection $f:A \to B$, then $A$ is finite and $card(A) \leq card(B)$ Hey, happy to help. Glad you get it! May 2 comment If $A,B$ are sets and $B$ is finite, and there is an injection $f:A \to B$, then $A$ is finite and $card(A) \leq card(B)$ $A$ is in bijection with its image in $g\circ f$, do you know what that means? It means, that $A$ maps bijectively to the subset of $[n]$ that is precisely $f\circ g (A)$ May 2 comment If $A,B$ are sets and $B$ is finite, and there is an injection $f:A \to B$, then $A$ is finite and $card(A) \leq card(B)$ I didn't say it is bijective. There is a bijection between $A$ and a subset of $[n]$ May 2 answered If $A,B$ are sets and $B$ is finite, and there is an injection $f:A \to B$, then $A$ is finite and $card(A) \leq card(B)$ May 2 comment Denesting Radicals with two different radicands Even for your example, the equations you have to solve are nasty. May 1 comment Assuming that the sum of the angles of any triangle is 180, how can I deduce Euclid's 5th postulate? I am not using that definition, I am using this one: If a line segment intersects two straight lines forming two interior angles on the same side that sum to less than two right angles, then the two lines, if extended indefinitely, meet on that side on which the angles sum to less than two right angles. May 1 comment Assuming that the sum of the angles of any triangle is 180, how can I deduce Euclid's 5th postulate? The OP must have updated the question while I was typing my answer. May 1 answered Assuming that the sum of the angles of any triangle is 180, how can I deduce Euclid's 5th postulate? Apr 9 awarded Nice Question Mar 10 awarded Popular Question Dec 20 awarded Yearling Oct 30 awarded Enlightened Oct 30 awarded Nice Answer Oct 20 awarded Popular Question Aug 4 comment How to prove that a $3\times 3$ Magic Square must have $5$ in its middle cell? very useful, thank you Jul 17 comment Fractional order Riemann Stieltjes integral No i have not heard of that integral Jul 17 comment Fractional order Riemann Stieltjes integral Oh ok I'm sorry Apr 12 awarded Inquisitive