Find the number of onto functions
- Anindya Biswas
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Let $A$ and $B$ be finite sets. If the number of elements in $A$ is $|A|=k$ and number of elements in $B$ is $|B|=n$ Find the number of onto functions (surjective functions) from $A$ to $B$ in terms of $n$ and $k$.
"If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is."
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- Mehrab4226
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Re: Find the number of onto functions
From $A$ there can be at most one line from each element. Because it is a figure of a function. Any element of $A$ producing more than one line will contradict the fact that it is a function.
The Mathematician does not study math because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful.
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- Anindya Biswas
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Re: Find the number of onto functions
Sorry to say, but you overcounted.Mehrab4226 wrote: ↑Tue Mar 16, 2021 8:00 pmThe reasoning can be a little difficult to understand for my bad solution writing. If you find any problems please post it.
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Hint :
"If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is."
— John von Neumann
— John von Neumann
- Mehrab4226
- Posts:230
- Joined:Sat Jan 11, 2020 1:38 pm
- Location:Dhaka, Bangladesh
Re: Find the number of onto functions
Thanks, I really didn't notice the overcounting
.Since You said there will be summation and principle of inclusion-exclusion, this should be it,
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The Mathematician does not study math because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful.
-Henri Poincaré
-Henri Poincaré