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Sep
18
comment How do you read the symbol “$\in$”?
no "its domain" relates to the variable, the domain is the set of values that the variable can take.
Sep
17
comment Elementary set problem
Try to start with left to right implication, and find a function $f$ that works.
Sep
17
comment We are given $f: X \rightarrow P(X)$, $f(x) = X\backslash\{x\}$, and $X$ is a set. Is the function injective, surjective, bijective?
@RobinGoodfellow I don't think it would be surjective, because $P(\emptyset)$ has one element.
Sep
17
comment We are given $f: X \rightarrow P(X)$, $f(x) = X\backslash\{x\}$, and $X$ is a set. Is the function injective, surjective, bijective?
Therefore, "Nothing is mapped to $X$" is more general
Sep
17
comment We are given $f: X \rightarrow P(X)$, $f(x) = X\backslash\{x\}$, and $X$ is a set. Is the function injective, surjective, bijective?
Except if $X$ is a singleton ;)
Sep
17
answered We are given $f: X \rightarrow P(X)$, $f(x) = X\backslash\{x\}$, and $X$ is a set. Is the function injective, surjective, bijective?
Sep
17
comment Prove that if $deg(u)+deg(v) \geq n-1$ for every two non adjacent vertices $u$ and $v$ of $G$ then $G$ is connected and $diam(G) \leq 2$
yes that's it !
Sep
16
revised Prove that if $deg(u)+deg(v) \geq n-1$ for every two non adjacent vertices $u$ and $v$ of $G$ then $G$ is connected and $diam(G) \leq 2$
added 186 characters in body
Sep
16
comment Prove that if $deg(u)+deg(v) \geq n-1$ for every two non adjacent vertices $u$ and $v$ of $G$ then $G$ is connected and $diam(G) \leq 2$
$deg(u)+deg(v)$. I detailed the hint in the answer.
Sep
16
comment Prove that if $deg(u)+deg(v) \geq n-1$ for every two non adjacent vertices $u$ and $v$ of $G$ then $G$ is connected and $diam(G) \leq 2$
if not, then their neighbours partition a subset of $G\setminus\{u,v\}$. How big can the sum of their degrees be in this case?
Sep
16
comment Cantor's Diagonal Argument
The important aspect is that real numbers canot be described with finite strings.
Sep
16
answered Calculate the depth of water in the trough when it is exactly half full
Sep
16
answered Prove that if $deg(u)+deg(v) \geq n-1$ for every two non adjacent vertices $u$ and $v$ of $G$ then $G$ is connected and $diam(G) \leq 2$
Sep
16
comment Find all sets $X$ so that $A\cap X=B$ and $A\cup X=C$
do you mean $A\cup X=C$ ?
Sep
10
comment Number of components of the graph G.
one inequality is trivial. The other just says that "breaking" a component by removing a vertex can just split it into two components, not more. Try to prove it formally via paths.
Aug
19
answered What happens if the coefficients of polynomials are not taken from a field of real numbers?
Aug
3
comment Calculate the width and height of a rectangle, given its diagonal and area
you have all the information to compute what $(x+y)^2$ is. Therefore you can compute $x+y$, and deduce the perimeter. You don't need to find out what $x$ and $y$ are, knowing $x+y$ is enough.
Aug
2
answered Calculate the width and height of a rectangle, given its diagonal and area
Jul
24
comment Bijection between $\mathbb N^+ \times \mathbb R^+$ and $\mathbb R^+$
You just need bijections $\mathbb N\to \mathbb N^+$ and $\mathbb R^+\cup\{0\}\to \mathbb R^+$ (and the first gives the second by the way).
Jul
24
comment Bijection between $\mathbb N^+ \times \mathbb R^+$ and $\mathbb R^+$
it depends if "bigger" in the question means strictly bigger or $\geq$. Anyway it is not hard to go from one to the other with bijections.