Tagged Questions

1
vote
3answers
23 views

What do you use for your basis step when its domain is all integers?

Example: *For all integers$ n , 4( n ^2 + n + 1) – 3 n ^2$ is a perfect square what should i use? negative infinity? I know you can use a direct proof but what if theres an induction question with ...
-1
votes
0answers
28 views

Proof in Probability Distribution Functions

The number of heads a coin comes up tails when tossed n times is denoted by random variable X. Suppose that for each toss, the coin will appear heads with probability z. (a) The probability mass ...
-4
votes
1answer
56 views

Transformation Existence Proof: A Call for Critique [duplicate]

QUESTION Prove that there exists a $T:V\rightarrow W$ such that $N(T)=V'\subset V$ and $R(T)=W'\subset W$ ATTEMPTED ANSWER Let $V$ and $W$ be finite-dimensional vector spaces over $F$. Let ...
1
vote
0answers
51 views

Examining every mathematical result in purely formal, ZFC language.

My main interest is physics. However, being self-taught in mathematics for the most part, my proofs tend to be more intuitive than it is acceptable. Yet, I recognize my inaptitude in rigor, and I ...
1
vote
3answers
75 views

help for proving an equation by induction

For this equation: $$-1^3+(-3)^3+(-5)^3+\ldots+(-2n-1)^3=(-n-1)^2(-2n^2-4n-1)$$ how can I prove this by induction? When I set $n = 1$ for the base case I got: $$-1^3 + (-3)^3 + (-5)^3 + \ldots + ...
2
votes
2answers
150 views

Induction Proof: $\sum_{i=1}^{n+1} i \cdot 2^i = n \cdot 2^{n+2}+2 $

Prove by Mathematical Induction . . . $$\sum_{i=1}^{n+1} i \cdot 2^i = n \cdot 2^{n+2}+2 $$ for all $n \geq 0$ I tried solving it, but I got stuck near the end . . . a. Basis Step: $1\cdot 2^1 ...
4
votes
2answers
114 views

Why does this step work in this proof?

I'm trying to learn discrete math and am brushing up on proofs by reading Richard Hammack's Book of Proof. I'm tripped up on this proof... I understand that it's contrapositive, and why contrapositive ...
35
votes
2answers
698 views

Is it possible to prove a mathematical statement by proving that a proof exists?

I'm sure there are easy ways of proving things using, well... any other method besides this! But still, I'm curious to know whether it would be acceptable/if it has been done before?
26
votes
2answers
1k views

Proof by contradiction vs Prove the contrapositive

What is the difference between a "proof by contradiction" and "proving the contrapositive"? Intuitive, it feels like doing the exact same thing. And when I compare an exercise, one person proves by ...
1
vote
1answer
74 views

Dirichlets theorem on primes

Is there a proof of dirichlets theorem that does not require complex analysis?
1
vote
1answer
44 views

how can I proof the GLOBAL optimality of a problem where the feasible region is disjoint?

I want to minimize the following function. It has two variable, $x$ and $y$ are real. I want proof the global optimality. But the feasible region of the variables are disjoint. My question is, how can ...
4
votes
1answer
74 views

Proofs whose length depends on the input

This may be a question from proof theory, but I'm not sure, since I don't know any proof theory. What I will be asking about is what happens, if the length of a proof isn't fixed: I'm going to present ...
0
votes
2answers
125 views

is it possible to prove the method of mathematical induction itself?

Since the method of mathematical induction follows some sort of 'algorithm', would the method itself be provable? namely, give that the method of mathematical induction is as follows: if S is a ...
3
votes
0answers
185 views

What are various proofs good for?

There are plenty of questions around here, which are proven to be right or wrong in various ways. I wonder, what one can learn from these differing ways of how to prove something, despite the fact ...
2
votes
3answers
250 views

Impossibility theorems

I've been wondering how you go about proving an impossibility e.g. when I looked up Abel's impossibility theorem it says nothing about the proof and only restates the theorem when I'd like to know how ...