- elementary set theory - Suppose $A$ and $B$ are sets. Prove that $A . . .
Suppose A is subset of B Let X belongs to A then by hypothesis, X will belong to B Hence X belong to A and X belong to B implies that X belongs to A intersection B Accordingly A is subset of A intersection B But we know that A intersection B is always subset of A Hence A intersection B is equal to A On the other hand, suppose A intersection B is equal to A Then in particular, A is
- With finite $\mu$, suppose $f_n$ converges in measure to $f$, and for . . .
This is actually a part b), where part a) was to show $f\in L^2$ This was simple: as $f_n$ converges in measure to $f$, there exists a sub-sequence which converges
- How do I know when to use let and suppose in a proof?
I often use 'suppose' when my goal is to derive a contradiction, and 'let' when I instantiate a variable when I'm not going to derive a contradiction I'm not sure if this is standard
- Suppose $CA=I_n$ (the $n \times n$ identity matrix. Show that the . . .
Does this answer your question? Linear Algebra - Suppose $CA=I_n$ Show that the equation $Ax = 0$ has only the trivial solution
- Suppose $A$, $B$, and $C$ are sets. Prove that $A B ⊆ C \iff A ∪ C = B . . .
Suppose $A$, $B$, and $C$ are sets Prove that $A B ⊆ C \iff A ∪ C = B ∪ C$ Ask Question Asked 8 years, 3 months ago Modified 8 years, 3 months ago
- general topology - Suppose that $X$ is Hausdorff. Show that $X$ is . . .
The title ("Suppose that $X$ is Hausdorff Show that $X$ is locally path connected") is false, though the body is true You know considerably more about $X$ than just that it is Hausdorff
- Let $H$ be a subgroup of a group $G$ and suppose that $g_1,g_2 ∈ G . . .
I have now gotten answers for (a) implying (e) and (e) implying (d) I'm overthinking all of this and am still confused about (d) implying (c) and (c) implying (b) When it comes to (b) implying (a), I thought I was getting somewhere but it doesn't seem to be working
- linear algebra - Suppose $v, w \in V$ where $V$ is a vector space . . .
Your reasoning is fine, but your wording is a bit ugly, as you observe A better approach might be to suppose that there are two such values, and then show that they must be the same: Suppose that \begin {align} v + 3x = w \text { and} \\ v + 3x' = w \end {align} Subtracting the second equation from the first, we get \begin {align} 3x - 3x' = 0 \\ 3 (x - x') = 0 \text { (distributive law
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