How do I know when to use "let" and "suppose" in a proof?
2015年8月19日 · Suppose n and m are natural numbers" or "Let n and m be arbitrary natural numbers." The boundary between "let" and "suppose" feels blurry. When do I use "let" and "suppose" in a math proof?
Determine the probability that no guest will receive the proper hat.
Suppose that 4 guests check their hats when they arrive at a restaurant, and that these hats are returned to them in a random order when they leave. Determine the probability that no guest will receive the proper hat. My attempt: So I know that there are 4! ways of "arranging" the hats.
$G$ is a group, $H$ is a subgroup of $G$ such that $[G : H]=2
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vector spaces - Suppose $a \in \mathbb F, v \in V$, and $av=0
2018年1月7日 · Suppose B is a vector and equal to (a,b,c,d) 5. Checking my Understanding of and Motivation behind Tensors ...
Suppose that $a$ has order $15$. Find all of the left cosets of ...
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Probability with Loaded Dice. - Mathematics Stack Exchange
2014年11月22日 · The Question Suppose that a die is biased (or loaded) so that 3 appears twice as often as each other number but that the other five outcomes are equally likely. What is the probability that an odd
Compute the probability you reach $5$ tokens before running out.
2024年8月15日 · Suppose you have $3$ tokens for a betting game and your goal is to bring your fortune up to $5$ tokens before running out of tokens. You devised a bold betting strategy where every turn, you will bet as many tokens as possible against the house but not any more than necessary to bring you to $5$ tokens.
real analysis - Suppose $f: [a,b] \rightarrow \mathbb {R}$ is …
Suppose $f:[a,b] \rightarrow \mathbb{R}$ is bounded and continuous except at a single point $c\in(a,b)$. Prove that $f$ is Riemann in
Let $G$ be a finite Abelian group that has exactly one subgroup …
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If $\\gcd(a,b)= 1$ and $a$ divides $bc$ then $a$ divides $c\\
It seems you have in mind a proof that uses prime factorizations, i.e. the prime factors of $\,a\,$ cannot occur in $\,b\:$ so they must occur in $\,c.\,$ You should write out this argument very carefully, so that it is clear how it depends crucially on the existence and uniqueness of prime factorizations, i.e. FTA = Fundamental Theorem of Arithmetic, i.e. $\Bbb Z$ is a UFD = Unique ...