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1d
comment Combinatorial proof for $\sum_{k = 0}^n \binom {r+k} k = \binom {r + n + 1} n$
This question asks specifically about combinatorial proofs: math.stackexchange.com/questions/1408642/…
1d
comment Fermat's Combinatorial Identity: How to prove combinatorially?
See also: math.stackexchange.com/questions/1408642/…
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revised Proving that $e^{\pi}-{\pi}^e\lt 1$ without using a calculator
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1d
comment Combinatorial Proof for Binomial Identity: $\sum_{k = 0}^n \binom{k}{p} = \binom{n+1}{p+1}$
@MarkusScheuer Looking among linked and related questions it seems that there are several other questions about combinatorial proof of the same identity. For example: 321022, 497413 1332282. If needed, we can discuss this further in chat.
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revised Give the combinatorial proof of the identity $\sum_{i=0}^{n} \binom{k-1+i}{k-1} = \binom{n+k}{k}$
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1d
revised Fermat's Combinatorial Identity: How to prove combinatorially?
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1d
revised Combinatorial Proof for Binomial Identity: $\sum_{k = 0}^n \binom{k}{p} = \binom{n+1}{p+1}$
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2d
revised Does intermedia value theorem apply to continuity on open intervals?
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2d
comment Give an example of a function $f :X \to Y$ which is sequential continuous but not continuous where $X$ and $Y$ are some topological spaces.
Could you be more specific what you mean by algebraic example. The current wording of the question might lead to the impression that you only allow Zariski topology for $X$. (In which case the question can be solved by finding an example of a ring for which the Zariski topology is not sequential.
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comment Give an example of a function $f :X \to Y$ which is sequential continuous but not continuous where $X$ and $Y$ are some topological spaces.
I will add a few links to other post on this site which have examples of such functions: math.stackexchange.com/q/351987, math.stackexchange.com/q/745036 and perhaps also math.stackexchange.com/questions/53236 (this is a slightly different question).
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revised Give an example of a function $f :X \to Y$ which is sequential continuous but not continuous where $X$ and $Y$ are some topological spaces.
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revised Book recomendation for function sequences.
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2d
revised Finding Galois group of $K=\Bbb{Q}(\omega,\sqrt2)$, showing that $K=\Bbb{Q}(\omega\sqrt2)$, and finding $\operatorname{min}(\omega\sqrt2,\Bbb{Q})$
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revised Find $\operatorname{min}(\omega\sqrt{2},\mathbb{Q})$
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2d
revised Definition of locally convex topological vector space
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revised Example of Topological Vector Space
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2d
revised Show that $y_n=x_{\phi(n)}$, defines a Cauchy sequence.
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revised Show that from a group of seven people whose (integer) ages add up to 332 one can select three people with the total age at least 142.
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revised Intermediate Value Property and Discontinuous Functions
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27
revised A natural number has exactly 10 divisors including 1 and itself.How many distinct prime factors can this natural number have?
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