Reputation
295,446
Next tag badge:
990/1000 score
280/200 answers
Badges
27 288 582
Newest
 Nice Answer
Impact
~4.5m people reached

Oct
23
comment Proving there are at least $N$ surjective functions from $A$ to $B$
@Newb: It’s a sequence of $n-1$ distinct objects chosen from the set $A$, which has altogether $m$ members. How many ways are there to choose such a sequence? This is one of the basic counting tasks.
Oct
23
answered show that $f$ is continuous
Oct
23
comment Proving there are at least $N$ surjective functions from $A$ to $B$
@Newb: Can you answer the question at the end?
Oct
23
comment $\displaystyle \sup_{x\in X}(\displaystyle \sup_{y\in y}|f(x,y)|) = \displaystyle \sup_{y\in Y}(\displaystyle \sup_{x\in X}|f(x,y)|)$
@Castaroth: What about it? That’s what $u$ is.
Oct
23
comment Solve the following non-homogeneous recurrence relation:
@Kumar2: You’re welcome.
Oct
23
answered $\displaystyle \sup_{x\in X}(\displaystyle \sup_{y\in y}|f(x,y)|) = \displaystyle \sup_{y\in Y}(\displaystyle \sup_{x\in X}|f(x,y)|)$
Oct
23
revised $\displaystyle \sup_{x\in X}(\displaystyle \sup_{y\in y}|f(x,y)|) = \displaystyle \sup_{y\in Y}(\displaystyle \sup_{x\in X}|f(x,y)|)$
Improved formatting.
Oct
23
answered Demonstration of complete system of residual classes. (Demonstração de sistema completo de classes resíduais.)
Oct
23
answered Grade calculation
Oct
23
comment Propositional logic-Predicates
@user2715467: You’re welcome.
Oct
23
answered Propositional logic-Predicates
Oct
23
answered Do Hyperreal numbers include infinitesimals?
Oct
23
comment A few questions relating to counting for midterm practise exam?
@StackPWRequirmentsAreCrazy: You’re welcome!
Oct
23
comment A few questions relating to counting for midterm practise exam?
... members of $A$, say $a_1$ and $a_2$. But that means that $f(a_1)=b=f(a_2)$ and hence that $f$ is not one-to-one.
Oct
23
comment A few questions relating to counting for midterm practise exam?
@StackPWRequirmentsAreCrazy: No matter what the sets $A$ and $B$ are, if $|A|>|B|$, there can be no one-to-one function from $A$ to $B$. Suppose that $A=n$, $|B|=m$, $m>n$, and $f:A\to B$. For each $b\in B$ let $A_b=\{a\in A:f(a)=b\}$. The sets $A_b$ are pairwise disjoint, since $f$ cannot send any element of $A$ to two different elements of $B$, so every element of $A$ is in exactly one $A_b$. The sets $A_b$ are the pigeonholes, and you’re stuffing the elements of $A$ into them. There are $n$ elements of $A$ and only $m$ pigeonholes, so some $A_b$ has to contain at least two different ...
Oct
23
comment Intuition Behind The Hyperreals
@user1770201: Yes, each real is infinitely close to infinitely many different hyperreals. There are infinitely many infinitesimals, and if $x\in\Bbb R$, then $x+\epsilon$ is a hyperreal infinitely close to $x$ whenever $\epsilon$ is an infinitesimal.
Oct
23
comment Convergence of certain sequences in $\Bbb R^\omega$
@KangHoonYou: There is no reason to think so: $k$ is one of the $n$ coordinates that don’t have to be $0$.
Oct
23
comment Convergence of certain sequences in $\Bbb R^\omega$
@KangHoonYou: The rest of them are $0$. Suppose that $k\in\{1,\ldots,n\}$. If $\ell\ge m$, then by the definition of $m$ we know that $\ell\ge m_k$. What does this say about $\pi_k(x_\ell)$?
Oct
23
answered Prove by induction on strings
Oct
23
answered Intuition Behind The Hyperreals