Constructivists deny the law of the excluded middle. You might be interested in this. For my own part I don't have any affinity for constructivism alt...
Yes, Pythagoras gets credit for (but probably didn't personally have anything to do with) the proof that sqrt(2) is irrational. Is it proof by contrad...
What do you mean by existence? Have we proved the existence of the number 3? Of 1/3 = .333...? Of -6? Of i such that i^2 = -1? Of the quaternion 1 + i...
Of course despair is a mental health problem. But a person experiencing despair need not be a nihilist nor vice versa. There are two distinct things: ...
Depression can not be labeled by a philosophical position. It seems to me that being a nihilist could be very freeing; and I can well envision an ecst...
Haven't read the thread, just wanted to toss something out that I heard. The Occupy protests were about class issues. "Banks got bailed out, we got so...
Jeez I'm with @"jgill" here. This is a standard example from freshman calculus. The integral of 1/x from 1 to infinity is infinite and the integral of...
soph·ist /?säf?st/ * a paid teacher of philosophy and rhetoric in ancient Greece, associated in popular thought with moral skepticism and specious rea...
Well ok. What would you say is the volume of the solid of revolution of y = \frac{1}{x} between 1 and \infty when the curve is revolved around the x-a...
Haven't I seen this trolled around the Internet on at least two other forums? The answer in that SciAm article is perfectly satisfactory. In any event...
"The best argument against democracy is a five minute conversation with the average voter." -- Attributed to Winston Churchill, though it's hard to kn...
I wish people would stop saying that. The unit circle in the taxicab metric is a square. There's a picture of a square circle on this page. https://en...
Bombs away baby. This is what got liberals dancing in the streets. And we'll be staying in Afghanistan till the cows come home. Liberals just can't ge...
Maybe modal logic can offer some clues. For example there's a "necessarily true" operator, so the negation of that might be what you want. https://en....
Anything that everyone believes is probably wrong. The truth is, the real problem is underpopulation. The fertility rate in the West is below replacem...
I read the entire Talk thread and have concluded that I no longer have any idea what a Euclidean space is. LOL. However someone in that thread did ref...
Well, like I say, I'm not entirely sure what we're disagreeing about. And you did actually make me think that I could be missing some subtleties. I kn...
I'm going to gracefully bow out, or turn tail and run, as the case may be. I find myself passionately defending my side of an argument without even kn...
Detaching from the use of preferred origin and axial orientation? I just can't parse that at all. Yes, the ordered pair of real numbers (0,0). Yes, th...
That's like saying I'm going to the store for oranges but I need to buy fruit as well. Oranges are the fruit I need to buy. An inner product is an abs...
Oh my. I think that's hopelessly convoluted, where did you get it? Here's what Euclidean space is. My reference here is for example Calculus on Manifo...
Well those are not mutually exclusive. Of course we use geometric intuition to get the analytic approach off the ground, but that's true of everything...
That sounds right. I don't know much about affine spaces. But basically an affine space is a vector space that's "forgotten its origin" and you don't ...
I guess I don't follow your point. The historical evolution is well known, from Euclid to Descartes. And in modern math we start with a 2-dimensional ...
Sure, but I'm not following your point. The Pythagorean theorem goes back over a couple of thousand years, and Cartesian coordinates go back only to D...
There's a theory of proofs over uncountable alphabets but I don't know anything about it. But as I say, by complexity I think of complexity theory, an...
If you have a proof that space is continuous that would be a discovery on a par with the revolutions of Newton and Einstein. I just pointed out that M...
Chaitin has used complexity theory to prove a version of Gödel's incompleteness theorem. But I wonder if you're using complexity in a different way. H...
The integers are discrete. And if you have any space whatsoever that's made of points, you can define the distance between two points to be 1 if the p...
You mentioned sobriety checkpoints, and I went off-topic for a moment to express my ambivalence about them in my dual societal role as both a civil li...
No, the horn is not closed. There are many online calculus tutorials and classes available that explain the theory of limits. That's now how limits ar...
Do you have a cat? Because someone in control of your account typed: Not so? If it wasn't you, perhaps your cat used your keyboard while you were othe...
\frac{1}{\infty} = 0 in the extended real number system, which is always the implicit domain of integration problems. The Numberphile guy didn't menti...
As a civil libertarian I am always conflicted. On the one hand, sobriety checkpoints are unconstitutional as they are a search without probable cause....
If I'm understanding you, you're concerned that the unit interval contains infinitely many points. Is that correct? If so, how many points do you thin...
If I'm not mistaken, the part you object to is when he's proving that the cross-sectional area is infinite; that is, the area under 1/x from 1 to infi...
You should look at it from the paradoxical decomposition of the free group on two generators. There are Wiki pages on the subject. It's simple, it's n...
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