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zeroflank
  • Member for 2 years, 10 months
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27 votes
4 answers
21k views

A continuous, injective function $f: \mathbb{R} \to \mathbb{R}$ is either strictly increasing or strictly decreasing.

7 votes
2 answers
213 views

To show that $\operatorname{Rank}(\mathbf{A}-\mathbf{I})=\operatorname{Nullity}(\mathbf{A})$

  • 2,155
7 votes
1 answer
657 views

Is it true that if $f(f(x))$ is continuous and strictly decreasing then $f$ is continuous$?$

  • 2,232
7 votes
3 answers
744 views

If a function f has no jump discontinuities, does it have the intermediate value theorem property?

  • 1,562
5 votes
2 answers
629 views

Group homomorphisms and which of the following statements are true (NBHM-$2014$)

5 votes
3 answers
313 views

Let $\,f \colon \Bbb R \to \Bbb R$ be a continuous function such that $|f(x)-f(y)|\ge \frac12 |x-y|$

  • 6,452
4 votes
2 answers
109 views

Given $A$ is $6×6 $ real symetric matrix of rank $5$ , then to determine rank of $A^{2}+ A+I $

  • 2,155
4 votes
4 answers
4k views

$\lambda$ for which the function $f(x)=2x^3-3(2+\lambda)x^2+12\lambda x$ has exactly one local maxima and exactly one local minima

  • 1,112
3 votes
2 answers
68 views

Does $\bigcup_{n=1}^\infty \left(-\infty, 1-\frac{1}{n}\right) = (-\infty, 1)$?

3 votes
1 answer
219 views

convergence of a sequence of continuous nonnegative functions(TIFR GS 2014)

2 votes
1 answer
73 views

Can $f(x,y) = |x|^y$ be be made continuous?

  • 2,155
2 votes
2 answers
68 views

If $a<b$, the $\lim_{x\to a^+}f(x) \le \lim_{x\to b^-}f(x) $?

  • 3,230
2 votes
1 answer
3k views

How to show that limit of $(x^3+y^3)/(x-y)$ does not exist at origin?

  • 2,155
1 vote
1 answer
601 views

Number of scalar addition required to compute P(QR) ,where P,Q,R be matrices or order $3× 5,5×7,7×3$

  • 2,155
1 vote
1 answer
220 views

To determine basis for $V \cap W$

  • 2,155
1 vote
1 answer
386 views

If $N$ is a normal subgroup of $G$ then not necessarily $\varphi(N)$ is a normal subgroup of $G'$

1 vote
1 answer
151 views

Finding infinite unions and intersections of $(1-1/k,2+1/k]$

1 vote
1 answer
417 views

Number of characteristic polynomial?

  • 171
1 vote
0 answers
80 views

Let $P$ be the set of all permutations in $S_{6}$ that can be expressed as a product of a multiple of $4$ transposition then $|P|$ is....$?$

  • 2,232
0 votes
1 answer
74 views

Real analysis problem from sequences?

0 votes
1 answer
73 views

Possible order of an element in a group

  • 2,056
0 votes
2 answers
686 views

In which of the following cases is there no continuous function from the set $S$ onto the set $T$?

  • 2,232
0 votes
1 answer
252 views

Stokes' theorem on intersection of $ x^2+y^2+z^2=1$ and $x+y=0$

  • 2,183