# Tagged Questions

For questions about the formulation of a proof, not about the mathematics behind it.

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### Prove $3+ 5 \sqrt {2}$ is irrational

Prove $3+ 5 \sqrt{2}$ is irrational. I have some ideas about this proof, but I am not quite finished. I understand being irrational means the number would not be in the form of $\frac pq$. I have ...
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### Leibniz Notation for the Derivative of a Function

I am writing a professionally-written proof, and I have come across a bit of an issue regarding how to write the derivative of a function $H(t)$ with respect to $t$. Is $\frac{dH}{dt}$ an acceptable ...
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### Proving $\sqrt{2}x-\sqrt{x^{2}+1} \geq \frac{\sqrt{2}}{2}\ln{(x)}$

How can I prove that $$x\sqrt{2}-\sqrt{x^{2}+1} \geq \frac{\sqrt{2}}{2}\ln{(x)}$$ It's a derivation-based process if I remember correctly, however I was unable to prove it correctly.
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### Prove that a sequence is bounded/unbounded

I'm trying to do a maths problem which requires me to determine whether a sequence is bounded or unbounded and then it wants me to prove my answe. I know that it's bounded but I've no idea how to ...
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### How to define two functions in a clear and standard way?

I am working on a question and before I ask it, I wanted to get help in defining two functions clearly in a standard way. Here are the two functions: $f(a,x,p)$: count of the number of pairs $k,k+2$...
### Proving $\cos(x)^2+\sin(x)^2=1$
I need to prove that $\cos(x)^2+\sin(x)^2=1$ Here's how I started (using the Cauchy product): \begin{align} \cos(x)^2+\sin(x)^2 &=\sum_{k=0}^{\infty}\sum_{l=0}^k(-1)^l\frac{x^{2l}}{(2l)!}(-1)^{k-...
### $3x + 1$ is even iff $5x-2$ is odd
I'm asked to prove 'Let $x \in Z$. $3x + 1$ is even iff $5x-2$ is odd'. I have the following proof techniques in my toolbox: trivial/vacuous proofs (not so relevant in this case), direct proof and ...