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?

Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

2015年1月25日 · Recently I learned an amazing thing. Suppose you are given a number and you have to find how many positive divisors it has. What would you do ? Solution: Suppose you select $12$. It has $1,2,3,4,6,12$ as its divisors; so, total number of divisors of $12$ is $6$. Now the method I learned:

2018年3月19日 · $\begingroup$ The conditional probability that we select a heart on the second draw given that we have selected a red card on the first draw is the probability of selecting a red card on the first draw and a heart on the second draw divided by the probability of selecting a red card on the first draw.

2019年12月8日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

2017年8月14日 · In Section 5.5.5 of Boyd's book "Convex Optimization", the book states that the primal problem can be solved by the dual problem. More precisely, suppose we have strong duality and an optimal $\{\lambda^{\ast}, \nu^{\ast} \}$ is known. Suppose that the minimizer of $\mathcal{L} (x,\lambda^{\ast}, \nu^{\ast})$, i.e., the solution of

For part 1, if there were a subsequence that didn't converge to the same limit, then we could find a neighborhood around the original point such that infinitely-many subsequence terms were outside the neighborhood.

2017年4月17日 · $\begingroup$ @Hi-Angel: Suppose you toss two coins (call them A and B) at the same time. What is probability that at least one of them shows heads? This is asking about the union. What is the probability that both show heads? This is …

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2015年5月14日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.