In this answer I used some symmetry to show that
$$
\int_0^1 \frac{dx}{x+ \sqrt{1-x^2}} = \frac \pi 4.
$$
Then I thought about whether I could make it simpler by avoiding trigonometric substitutions, like this:
$$
y = \sqrt{1-x^2}
$$
Therefore
$$
y^2+x^2=1 \tag a
$$
From the symmetry in line $(\t...
One of my partners often makes the same argument when we're discussing something.
If we're talking about doing A, he'll respond: if you want to do A, then why not do B, C and D too? And if we're not going to do B, C, and D, then we shouldn't be doing A either.
Every time he makes this argument ...
The tag fallacies has been created recently. Currently, there are two questions using this tag. The tag-info is empty.
Is this tag going to be useful? Are there things which are not covered by already existing tags paradoxes and fake-proofs?
If the tag is kept, what type of questions should it...
One of my partners often makes the same argument when we're discussing something.
If we're talking about doing A, he'll respond: if you want to do A, then why not do B, C and D too? And if we're not going to do B, C, and D, then we shouldn't be doing A either.
Every time he makes this argument ...
The tag fallacies has been created recently. Currently, there are two questions using this tag. The tag-info is empty.
Is this tag going to be useful? Are there things which are not covered by already existing tags paradoxes and fake-proofs?
If the tag is kept, what type of questions should it...
