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  • 0 posts edited
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  • 30 votes cast
Mar
30
accepted Finding the dual of a LP
Mar
30
answered Finding the dual of a LP
Mar
11
asked Finding the dual of a LP
Jan
24
asked Size of coefficients of polynomials that satisfy a Chebyshev-like extremal property
Jul
3
accepted A closed form for the coefficients of Chebyshev polynomials
Jul
2
asked A closed form for the coefficients of Chebyshev polynomials
Sep
28
revised Use induction to prove that a function is not one to one
Further explained the process of restricting f and renamed variables.
Sep
28
comment Use induction to prove that a function is not one to one
By the way, the notation is defined this way: for all integers $N$, $[N]:=\{1,...,N\}$.
Sep
28
comment Use induction to prove that a function is not one to one
For induction, you prove the base case (here, when $k=1$). Then assume the theorem holds for all $k<K$ and show that implies that the theorem holds for the next value of $k=K+1$. The inductive hypothesis in the above proof is that there is no one-to-one function $f:[K+1]\rightarrow [K]$. We want to show that this lack of existence of a 1-1 function from [K+1] to [K] implies the lack of existence of a 1-1 function from [K+2] to [K+1]. Use a proof by contradiction. Suppose such a 1-1 function $f$ exists, and use it to construct a function that is 1-1 from [K+1] to [K], a contradiction.
Sep
28
comment Use induction to prove that a function is not one to one
Are you asking about the second to last sentence?
Sep
28
answered Use induction to prove that a function is not one to one
Aug
28
awarded  Tumbleweed
Jul
20
awarded  Yearling
Jul
5
comment Sequence of natural numbers
I agree. The approach suggested by Tomas seems very promising.
Jul
5
revised Sequence of natural numbers
added 10 characters in body
Jul
5
answered Sequence of natural numbers
Jul
5
awarded  Critic
Jul
3
answered $A$ is a subset of $B$ if and only if $P(A) \subset P(B)$
Jan
26
awarded  Self-Learner
Aug
24
comment Theorems with an extraordinary exception or a small number of sporadic exceptions
Wouldn't theorems with no exceptions be in this list too? (Such as all integers are divisible by 1)?