Question

If $f(\frac{x+f(x)}{2})=x$, for all $x \in \Bbb R$, Prove that $f(x)=x$ for all $x\in \Bbb R$.

score 72 · Answer 1 · 2026-04-16 14:01:14

72

Views

If $f(\frac{x+f(x)}{2})=x$, for all $x \in \Bbb R$, Prove that $f(x)=x$ for all $x\in \Bbb R$.

Published on 16 Apr 2026 - 14:01

score 1k · Answer 2 · 2026-04-11 11:42:42

1k

Views

Proof : Bolzano Weierstrass theorem

Published on 11 Apr 2026 - 11:42

score 101 · Answer 3 · 2026-04-15 01:14:45

101

Views

Why is $\lim_{x\rightarrow \infty}(1+\frac{a}{bx+c})^{dx+f}=e^{\frac{a\cdot d}{b}}$?

Published on 15 Apr 2026 - 1:14

score 799 · Answer 4 · 2026-04-12 04:39:25

799

Views

Prove that transitivity holds for "the cardinality of A does not exceed the cardinality of B".

Published on 12 Apr 2026 - 4:39

score 3.6k · Answer 5 · 2026-04-13 23:47:55

3.6k

Views

Show that the inverse of a projection matrix, when exists, is again a projection matrix.

Published on 13 Apr 2026 - 23:47

score 135 · Answer 6 · 2026-04-16 13:30:35

135

Views

Let $f_1,f_2,...,f_k$ be pairwise orthogonal nonzero vectors of $R^n$

Published on 16 Apr 2026 - 13:30

score 345 · Answer 7 · 2026-04-10 20:30:59

345

Views

Bernoulli numbers.

Published on 10 Apr 2026 - 20:30

score 3.7k · Answer 8 · 2026-04-11 08:38:58

3.7k

Views

find the probability mass function of a random variable X

Published on 11 Apr 2026 - 8:38

score 116 · Answer 9 · 2026-04-13 19:24:16

116

Views

Question on the proof to show that a jump function is discontinuous with the $\epsilon$-$\delta$-criterion

Published on 13 Apr 2026 - 19:24

score 120 · Answer 10 · 2026-04-16 22:34:34

120

Views

Clarification of Lemma $23.1$ from Munkres concerning the separation of a subspace. How do we know $A$ is open in $Y$?

Published on 16 Apr 2026 - 22:34

score 70 · Answer 11 · 2026-05-10 21:58:34

70

Views

Question about a proof of PA$_2$'s categoricity

Published on 10 May 2026 - 21:58

score 69 · Answer 12 · 2026-04-13 03:57:27

69

Views

One point differentiable function.

Published on 13 Apr 2026 - 3:57

score 293 · Answer 13 · 2026-04-15 01:01:16

293

Views

Lattice proof for C(n,r) = C(n-1,r) +C(n-1,r-1)

Published on 15 Apr 2026 - 1:01

score 2.3k · Answer 14 · 2026-04-11 21:18:55

2.3k

Views

How to prove the intersection of functions is a function

Published on 11 Apr 2026 - 21:18

score 60 · Answer 15 · 2026-04-15 06:16:33

60

Views

Showing there are Infinitely Many Pairs that Satisfy Certain Criteria...

Published on 15 Apr 2026 - 6:16

List Question

If $f(\frac{x+f(x)}{2})=x$, for all $x \in \Bbb R$, Prove that $f(x)=x$ for all $x\in \Bbb R$.

Proof : Bolzano Weierstrass theorem

Why is $\lim_{x\rightarrow \infty}(1+\frac{a}{bx+c})^{dx+f}=e^{\frac{a\cdot d}{b}}$?

Prove that transitivity holds for "the cardinality of A does not exceed the cardinality of B".

Show that the inverse of a projection matrix, when exists, is again a projection matrix.

Let $f_1,f_2,...,f_k$ be pairwise orthogonal nonzero vectors of $R^n$

Bernoulli numbers.

find the probability mass function of a random variable X

Question on the proof to show that a jump function is discontinuous with the $\epsilon$-$\delta$-criterion

Clarification of Lemma $23.1$ from Munkres concerning the separation of a subspace. How do we know $A$ is open in $Y$?

Question about a proof of PA$_2$'s categoricity

One point differentiable function.

Lattice proof for C(n,r) = C(n-1,r) +C(n-1,r-1)

How to prove the intersection of functions is a function

Showing there are Infinitely Many Pairs that Satisfy Certain Criteria...

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