Questions tagged [induction]
The induction tag has no usage guidance.
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Bound for the Malliavin derivative
Recently, I read the article Quantitative normal approximations for the stochastic fractional heat equation and I have a question in proof of Lemma 5.3. By using Lemma 5.3, they got
$$||D_{s,y}u(t,x)|...
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Prove that every group $G$ with $p^n$ ($n\ge4$) elements and center with $p$ elements has an abelian subgroup of order $p^3$ [closed]
Prove that every group $G$ with $p^n$ ($n\ge4$) elements and center with $p$ elements has an abelian subgroup of order $p^3$
I'm new in this forum so I hope I haven't made any mistake.
I have to ...
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A summation involving fraction of binomial coefficients
I need to prove the following statement.
Let $ n, g, m, a ,t$ be integers. Prove that the following statement is true for all $ n \geq g(1+2m)+1 $, $ g\geq 2t $, $ m\geq t $, $ 0\leq a <t $, and $ ...
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Summation of rows of a matrix P^k is decreasing with the power k
I have the following $(n+1)\times (n+1)$ matrix
$$P = \begin{bmatrix}
f(0) & g(0) & 0 & 0 & 0 & \dots & 0\\
f(1) & 0 & g(1) & 0 & 0 & \dots & 0\\
f(2) &...
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Terminology associated with mathematical induction
In "Number: The Language of Science" (1930), Tobias Dantzig refers to what we call the base case of mathematical induction as "the induction step" (and refers to what we call the ...
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Zorn's lemma: old friend or historical relic?
It is often said that instead of proving a great theorem a mathematician's fondest dream is to prove a great lemma. Something like Kőnig's tree lemma, or Yoneda's lemma, or really anything from this ...
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Largest eigenvalue of a Laplacian matrix to lower bound the prime counting function? (Recursive formula for prime pi?)
Let $L_n$ be the Laplacian matrix of the undirected graph $G_n = (V_n, E_n)$ (which is defined here: Why is this bipartite graph a partial cube, if it is? ) with sorted spectrum:
$$\lambda_1 (G_n) \ge ...
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What does "sup" mean in the context of a w type? [closed]
Like the constructor for a W type is called "sup" but I don't know what that expands to. Is it super? maybe supremum? Or is it just an arbitrary name, like dynamic programming?
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Induction for quantum group
I am confused about a claim in the article Representation of quantum algebras by Henning Haahr Andersen, Patrick Polo and Wen Kexin. I probably misunderstood a definition, but I found two claims about ...
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Mathematical induction and the counting function on $\mathbb{Z}_p^2$
Let $\mathbb{Z}_p$ be a finite field of order $p$ and $\mathbb{Z}_p^2$ be a $2$-dimensional vector space over $\mathbb{Z}_p$. We consider the distance $\lVert \cdot \rVert:\mathbb{Z}_p^2\to \mathbb{Z}...
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Nicely motivated papers or book chapters on the formula for the sum of the $k$-th powers of the first natural numbers [closed]
Do you know of a text where I can find a nicely motivated proof of the formula for $1^{k}+2^{k}+\cdots+n^{k}$?
At the very beginning of page 68 of Professor H. S. Wilf's generatingfunctionology, one ...
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How to structure a proof by induction in a maths research paper?
I am 16 years old at the time of writing (so I have no supervisors to seek advice from) and I have written a mathematics research paper, which I plan on submitting to a journal for publication. I ...
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Seek help to formalize an argument to positiveness of function defined inductively by integral [closed]
I have on domain $[0,\infty)$ a known and positive function $f(x)$ and two unknown functions $g(x), h(x)$ that start positive when $x=0$.
I also know that if $h(x)$ is positive, then $g(x)$ is also ...
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Can you define inductive data types over categories other than Set?
Can you define inductive data types over categories other than $\mathbb{Set}$?
What does it look like? How about for a specific example like the category of monoids? If you were clever could you write ...
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Is the Frog game solvable in the root of a full binary tree?
This is a cross-post from math.stackexchange.com$^{[1]}$, since the bounty there didn't lead to any new insights.
For reference,
The Frog game is the generalization of the Frog Jumping (see it on ...
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