List questions from induction

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Prove that exists Gray Codes of length $\lceil \log_2 k \rceil$ for any positive integer $k$

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An exercise from Shapiro's Abstract Algebra

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Subset Inequality Problem

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Prove that any positive integer can be written as sum of distinct numbers from $1,2,3,4,5,10,20,\ldots$

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How do I complete this proof by induction?

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Proof Verification: $2^n+1 \leq 3^n$

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Proving the sum of length of a unique path in a tree is less than equal to $n$ choose $2$.

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Symmetric difference of a set and its n-th preimage

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A (Faulty) Proof that $(-1)^{n}$ is Monotone

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Peano axiom of induction with "no junk"

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If $x$ and $y$ are numbers such that $x + y, x^2 + y^2, x^3 + y^3$ and $x^4 + y^4$ are all integers. Show that $x^n + y^n$ is an integer.

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Breaking the implication chain in inductive reasoning

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Proving $ {1 \over 2\sqrt1} + {1 \over 3\sqrt2} + \dots + {1 \over (n+1)\sqrt n} \lt 2$ using induction

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General Solution to Secular Terms in ODE System: Inductive Proof

Published on 10 Apr 2026 - 18:33

List Question

Stuck on mathematical induction proof at inductive step

Prove that exists Gray Codes of length $\lceil \log_2 k \rceil$ for any positive integer $k$

An exercise from Shapiro's Abstract Algebra

Subset Inequality Problem

Prove that any positive integer can be written as sum of distinct numbers from $1,2,3,4,5,10,20,\ldots$

How do I complete this proof by induction?

Proof Verification: $2^n+1 \leq 3^n$

Proving the sum of length of a unique path in a tree is less than equal to $n$ choose $2$.

Symmetric difference of a set and its n-th preimage

A (Faulty) Proof that $(-1)^{n}$ is Monotone

Peano axiom of induction with "no junk"

If $x$ and $y$ are numbers such that $x + y, x^2 + y^2, x^3 + y^3$ and $x^4 + y^4$ are all integers. Show that $x^n + y^n$ is an integer.

Breaking the implication chain in inductive reasoning

Proving $ {1 \over 2\sqrt1} + {1 \over 3\sqrt2} + \dots + {1 \over (n+1)\sqrt n} \lt 2$ using induction

General Solution to Secular Terms in ODE System: Inductive Proof

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