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MathNerd
  • Member for 8 years, 7 months
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9 votes

Why are real numbers useful?

7 votes
Accepted

Exercise books in analysis

2 votes
Accepted

For any integer $n\geq 1$, define $\sin_n=\sin\circ ... \circ \sin$ ($n$ times). Prove that $\lim_{x\to 0}\frac{\sin_nx}{x}=1$ for all $n\geq 1$

2 votes

Proving $f'(0)=0$ if $\lim_{x\to0}f(x)/x^2$ exists and is finite

1 vote
Accepted

Updating the Definition of Limit of a Sequence to take in consideration sequences that are not defined for some finite number of natural numbers

1 vote

Prove that there is no function $f:\Bbb{R}\to\Bbb{R}$ with $f(0)>0$ such that $\forall x,y\in\Bbb{R}, f(x+y)\geq f(x)+y f(f(x))$

1 vote
Accepted

A question about fixed-point iteration sequence of a two times continuously differentiable function

1 vote

Prove that if $f:[a,b]\to\Bbb{R}$ is one to one and has the intermediate value property, then $f$ is strictly monotone

1 vote
Accepted

Find all functions $ f:\Bbb{R}\to\Bbb{R}$ with the intermediate value property such that $\exists 1\leq n\in\Bbb{Z}, f^n(x)=-x$

0 votes

A problem on balls of different colors randomly selected from a box.

0 votes

A question about different pairs that are formed from a set of 16 different poeple such that...

0 votes

Parametric Representation for a Square with Side $1$ Centered at the Origin as a Function of the Angle Measured from the Positive $x$-Axis

0 votes

Minimum number of steps required to visit every corner of a rectangular grid

0 votes

Sigma algebra of a collection of sets.

0 votes

Can we plug a linear sequence of real numbers into the sine function such that the resulting sequence will be a one-to-one sequence?

-1 votes
Accepted

Building neighborhoods around arbitrary real numbers that will contain "minimal" number of elements from the sequence $a_n=n\sin \frac{\pi n}{4}$