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- What is infinity divided by infinity? - Mathematics Stack Exchange
I know that $\\infty \\infty$ is not generally defined However, if we have 2 equal infinities divided by each other, would it be 1? if we have an infinity divided by another half-as-big infinity, for
- Difference between ≈, ≃, and ≅ - Mathematics Stack Exchange
In mathematical notation, what are the usage differences between the various approximately-equal signs "≈", "≃", and "≅"? The Unicode standard lists all of them inside the Mathematical Operators B
- Justifying why 0 0 is indeterminate and 1 0 is undefined
0 0 = x 0 0 = x 0x = 0 0 x = 0 x x can be any value, therefore 0 0 0 0 can be any value, and is indeterminate 1 0 = x 1 0 = x 0x = 1 0 x = 1 There is no such x x that satisfies the above, therefore 1 0 1 0 is undefined Is this a reasonable or naive thought process? It seems too simple to be true
- calculus - Finding $\int x^xdx$ - Mathematics Stack Exchange
The integral ∫ xxdx can be expressed as a double series I asked about this series form here and the answers there show it is correct and my own answer there shows you can differentiate this back to get a power series for xx: ∫xxdx = ∞ ∑ n = 1n − 1 ∑ k = 0xnlogk(x)(− 1)1 + n + k nn − k k!
- epistemology - Fallacy by Sherlock Holmes Eliminate the impossible . . .
Well, the fallacy would not be in Sherlock Holmes line; that remains perfectly valid The fallacy would be in the hybris of the person who did not carefully conduct an exhaustive search for alternatives In order to use "whatever remains, however improbable, must be the truth" you must exhaust the space of possibilities first If you didn't do that, you are not entitled to appeal to Sherlock
- How does wealth corrupt someone? - Philosophy Stack Exchange
"A new study calls into question earlier research suggesting that people of higher socioeconomic status are less generous and more selfish than others", GGM Wealth and Virtue is a short survey of takes from Aristotle to Hayek, they are not all negative Ward has a book Wealth, virtue, and moral luck from Christian perspective
- Why is $\\infty\\times 0$ indeterminate? - Mathematics Stack Exchange
"Infinity times zero" or "zero times infinity" is a "battle of two giants" Zero is so small that it makes everyone vanish, but infinite is so huge that it makes everyone infinite after multiplication In particular, infinity is the same thing as "1 over 0", so "zero times infinity" is the same thing as "zero over zero", which is an indeterminate form Your title says something else than
- Taylor series of $\\ln(1+x)$? - Mathematics Stack Exchange
You got the general expansion about x = a Here we are intended to take a = 0 That is, we are finding the Maclaurin series of ln(1 + x) That will simplify your expression considerably Note also that (n − 1)! n! = 1 n The approach in the suggested solution also works We note that 1 1 + t = 1 − t + t2 − t3 + ⋯
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