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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
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10
awarded  Popular Question
Dec
20
awarded  Yearling
Oct
30
awarded  Enlightened
Oct
30
awarded  Nice Answer
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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