ogogmad

37 ms·

661.
by ogogmad 4y ago
Your definition would rule out finite sets. You don't need a bijection. A surjection from the natural numbers suffices. In plain English, you need to construct an infinite sequence (a,b,c,d,...) which (i) consists of elements of a set
662.
by ogogmad 4y ago
> A lot of people thought if you can't force everyone - it's a suckers game. Why should I isolate when other people aren't, and the effects are minimized - etc. The perfect tragedy of the commons. It's why we need gov
663.
by ogogmad 4y ago
I don't know if you know this: In a topos in which Countable Choice holds, the Cauchy reals are isomorphic to the Dedekind reals. In other words, it doesn't matter whether the reals are constructed via Cauchy sequences or Dedekind
664.
by ogogmad 4y ago
In this particular foundation, the set of real numbers is countable. It is "the" set of real numbers in that particular foundation.
665.
by ogogmad 4y ago
> But inside the model there really isn't a bijection between the sets of naturals and reals No. Inside the model, there is exactly such a surjection. We don't care what happens outside of it. Maybe you already knew this, but
666.
by ogogmad 4y ago
There is only a "the" set of real numbers if there is a "the" foundation of mathematics. https://www.ams.org/journals/bull/2017-54-03/S0273-0979-2016... I chose that title out of a combina
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by ogogmad 4y ago
There's more than one way to prove the real numbers uncountable. All of them assume something though! https://link.springer.com/content/pdf/bbm:978-1-4614-8854-5/... There's a recursive subdivision
668.
by ogogmad 4y ago
And it became the highest voted comment here. Draw your own conclusion about this place.
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by ogogmad 4y ago
You invoke LEM when you can't decide computationally whether a proposition is true or not. If you could decide, you wouldn't invoke it. Admittedly, I exaggerated a bit because my comments were already too long. You can always prov
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by ogogmad 4y ago
OK listen, spekcular. You haven't responded to any of my comments about constructive logic. > But, historically speaking, that was not what people had in mind. You have opinions about what you'd like from foundations. They are
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by ogogmad 4y ago
Nobody's comparing the aesthetics of sets to types. That's not the point... People want mathematical proofs to automatically determine programs, or to be more than just proofs somehow. They want to exploit the capabilities of cons
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by ogogmad 4y ago
OK, but that's in ZFC. You don't have to do things that way. Not everything needs to be an encoding of a thing. Sometimes we want a thing to be the actual thing. You're very dogmatic about what people should accept from a fou
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by ogogmad 4y ago
Constructive logic is logic without the Law of Excluded Middle. It is the part of mathematics that is actually relevant to computing. HoTT serves as a good foundation for constructive logic; perhaps better than any other. Set theory (like Z
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The countable set of real numbers [video](youtube.com)
42 points by ogogmad 4y ago|44 comments
675.
by ogogmad 4y ago
Your comment demonstrates a lack of reading comprehension. I don't care what we "let" people do, as I stressed in my comment. The actual point was that it's not as "safe" as many of its most blinkered advocates
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by ogogmad 4y ago
There's still a chance that cannabis might trigger schizophrenia, especially among people who start very young. This is at right angles to the legalisation debate, because alcohol and tobacco are likely to be even more harmful. It rema
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Listing applications of the SVD(mathoverflow.net)
1 points by ogogmad 4y ago|0 comments
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by ogogmad 4y ago
"Rule of thumb" has just joined blacklist and quantum supremacy. If she yelled at you, please complain about her.
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by ogogmad 4y ago
> The argument looks like it's based on large n asymptotics, so even assuming everything works correctly the strongest statement they can hope to show is that the theorem is true for all n > n_0, where n_0 is some large constant.
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by ogogmad 4y ago
The tone of your comment is pretty harsh. What kind of 2nd-order evidence do you see? And why did you learn from the introduction that makes you so sure? It's only an introduction, which might only give you an oversimplified summary of
681.
by ogogmad 4y ago
Is Battleship Potemkin in the PD in both Europe and the US?
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by ogogmad 4y ago
When?
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by ogogmad 4y ago
For people who have time to burn being uselessly pedantic, is this a topologist's world map up to homotopy equivalence or homeomorphism? [edit] I think I get how to encode a hypergraph as a topological space. Let S be a set consisting
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by ogogmad 4y ago
What triggered this?
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by ogogmad 4y ago
The accusations were partly based on him cosying up with terrorists, from Hamas, Iran, etc. Is it too much to ask that a candidate for Prime Minister should respect the Rule of Law? There's also his support for Chavez/Maduro, his
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by ogogmad 4y ago
But does it accidentally words as much?
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by ogogmad 4y ago
If you read this carefully... One way to prove that there are infinitely many prime numbers is by using the concept of contradiction. Suppose that there are only a finite number of prime numbers, say p_1, p_2, ..., p_n. Then consider th
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by ogogmad 4y ago
This is reaching you late, but you're not shadow-banned.
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by ogogmad 4y ago
I thought you were anti-Semitic dog-whistling. I stand corrected.
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by ogogmad 4y ago
The only commonality between those 3 people is that they're Jewish. There are good and bad people from every race and gender. "Russian" in the case you're talking about is not an ethnicity, so it's a false equivalen

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