Newbetuts

If $G$ is a connected graph with $n$ vertices and $n - 1$ edges then $G$ is a tree, using Induction.

Proving infinite wedge sum of circles isn't first countable

For all real numbers x, if x −⌊ x ⌋≥ 1/2 then ⌊2x ⌋= 2⌊x ⌋+ 1.

Prove that all subsets of countable sets are countable

If $a+b+c$ divides the product $abc$, then is $(a,b,c)$ a Pythagorean Triple?

"$n$ is even iff $n^2$ is even" and other simple statements to teach proof-writing

Prove $\frac{1}{2} + \cos(x) + \cos(2x) + \dots+ \cos(nx) = \frac{\sin(n+\frac{1}{2})x}{2\sin(\frac{1}{2}x)}$ for $x \neq 0, \pm 2\pi, \pm 4\pi,\dots$

The role of 'arbitrary' in proofs

APICS Mathematics Contest 1999: Prove $\sin^2(x+\alpha)+\sin^2(x+\beta)-2\cos(\alpha-\beta)\sin(x+\alpha)\sin(x+\beta)$ is a constant function of $x$

Why isn't this approach in solving $x^2+x+1=0$ valid?

Show $f:\Bbb{R}\to\mathbb{R}$ given by $f(x)=2x\cdot |x|+3$ is injective and surjective.

Show that $e^n>\frac{(n+1)^n}{n!}$ without using induction.

Why are proofs not written as collections of logic symbols but are instead written in sentences? [duplicate]

Show that $[2x]+[2y] \geq [x]+[y]+[x+y]$

Proof for showing that $\text{dim}(W)\leq \text{dim}(V)$

How $b>a \lor a \leq 0 \implies \max⁡(b,0)-\max⁡(\min⁡(a,b),0) \geq 0$?

New posts in proof-writing

Show that $\{\cup_{n\in K} (n, n+1]: K \subset \mathbb{Z}\}$ is a $\sigma$-algebra on $\mathbb{R}$

circular reasoning in proving $\frac{\sin x}x\to1,x\to0$

Can you string together inequalities and equalities into a single statement?

Developing Kepler's first law from the two-body problem

If $G$ is a connected graph with $n$ vertices and $n - 1$ edges then $G$ is a tree, using Induction.

Proving infinite wedge sum of circles isn't first countable

For all real numbers x, if x −⌊ x ⌋≥ 1/2 then ⌊2x ⌋= 2⌊x ⌋+ 1.

Prove that all subsets of countable sets are countable

If $a+b+c$ divides the product $abc$, then is $(a,b,c)$ a Pythagorean Triple?

"$n$ is even iff $n^2$ is even" and other simple statements to teach proof-writing

Prove $\frac{1}{2} + \cos(x) + \cos(2x) + \dots+ \cos(nx) = \frac{\sin(n+\frac{1}{2})x}{2\sin(\frac{1}{2}x)}$ for $x \neq 0, \pm 2\pi, \pm 4\pi,\dots$

The role of 'arbitrary' in proofs

APICS Mathematics Contest 1999: Prove $\sin^2(x+\alpha)+\sin^2(x+\beta)-2\cos(\alpha-\beta)\sin(x+\alpha)\sin(x+\beta)$ is a constant function of $x$

Why isn't this approach in solving $x^2+x+1=0$ valid?

Show $f:\Bbb{R}\to\mathbb{R}$ given by $f(x)=2x\cdot |x|+3$ is injective and surjective.

Show that $e^n>\frac{(n+1)^n}{n!}$ without using induction.

Why are proofs not written as collections of logic symbols but are instead written in sentences? [duplicate]

Show that $[2x]+[2y] \geq [x]+[y]+[x+y]$

Proof for showing that $\text{dim}(W)\leq \text{dim}(V)$

How $b>a \lor a \leq 0 \implies \max⁡(b,0)-\max⁡(\min⁡(a,b),0) \geq 0$?