I don't know what 'ungraded' means there, but there many many library shelves worth of articles and books in the philosophy of mathematics on the subj...
No. It just needs to be clear what the context is. As I mentioned, one of those is claimed as a mathematical definition. But it is not. Whatever your ...
You said you were distinguishing the mathematical notion from a metaphysical notion. You didn't say anything about the mathematical notion being a lay...
'P' for 'is an appearance' 'F' for 'is known in a filtered way' 'U' for 'is known in an unfiltered way' 'r' for 'our action' (1) Ax(Fx -> ~Ux) premise...
The theorem is: ~ExAy yex "It is not the case that there exists an x such that every y is a member of x." or, in context, "There is no set of which ev...
I made a mistake in this thread. I didn't know it then, but I know now, that I used the word 'onto' in a way that is not standard English, which got t...
What is your definition of 'all-inclusive' in this context? The theorem is: ~ExAy yex "It is not the case that there exists an x such that every y is ...
If there are no infinite sets, then there is no set of all the integers nor set of all the reals. But the observation about them could still hold in t...
No, that is plainly wrong. Both the set of natural numbers and the set of real numbers are transfinite sets. Why are you making pronouncements on a su...
Yes, a set of two lines is a countably (and finite) set. The set of points in a line is uncountable. And the union of the sets of points in any number...
If it is the sum of the issue, then the sum of the issue is meaningless until 'discrete' is given a definition. Meanwhile, the continuum is the pair <...
The cardinalities of the set of natural numbers and the set of real numbers are both infinite cardinalities, but not the same infinite cardinalities. ...
That is yet another variation on conflating the mathematics with personal undefined terminology. If only you would carefully read the mathematical tre...
1. is not the mathematical definition. 2. is not the mathematical definition, and it is in error by claiming to be so. / It's fine to make whatever ar...
If the context is mathematics, then usually the notion of 'infinite' is referenced per set theory. Of course, we are free to philosophize and use term...
The word 'opposite' has caused problems in this thread because it is not been defined. An undefined word that causes confusion is less than needed. We...
The notion that necessary implies impossible is, as reiterated, daft. So, we would not expect to find this as an axiom: Nq -> ~Pq But what about?: Nq ...
As to 'impossible': Yes, 'impossible' is the negation of 'possible'. df. Pq <-> ~N~q df. q is impossible <-> ~Pq / q is is necessary if and only if q ...
"No, the speaker might know that the book is in the car but choose to be coy, though literally honest and correct, in saying "The book might be in the...
Wrong. We prove that any decimal expansion that has an infinitely repeating part represents a rational number. We may also conclude that 0.9 is ration...
It was a steep you mentioned in defense of your argument. My criticism of that step is correct. And you presented your program to me also in defense o...
What I said is true. Yes, and it was axiomatized by set theory. What I said is true: From the axioms of set theory, we derive the theorems of calculus...
Set theory is abstract. It doesn't have hotels. To be more exact, I should say that from an imaginary analogy to set theory, you impose an incoherent ...
You don't like that mathematics for the sciences doesn't comport with your understanding of impossible fictional realms. Yeah, that's a real dagger in...
Then it will miss outputting one of the 9s. You can't have cake and eat it too. If it runs only finitely many steps but outputs the 1, then it skips a...
You can write whatever you like, but my point, as seen in context, is that it's not a program to print all the entries in the sequence. Consider the a...
No he's not. The halting problem is not that there are programs that don't halt. But rather that there is no program to decide whether any given progr...
Depends on the exact interpretation of a given definition. If taken literally in the sense of 'practices complete abstinence' then drinking alcohol ev...
Whatever you have in mind, it's not a program. If P is a program to print the entries in a denumerable sequence, then for each entry, there is step at...
Refer to the subject of non-standard analysis in mathematical logic (starting with Abraham Robinson), or, with a different method, internal set theory...
I didn't know whether you're talking about yourself or about me. (And I couldn't resist the wordplay.) In any case, if your point is that you're bette...
The point is not to insult, but rather to flag the situation. Usually cranks are not trolls, since they are sincere, though horribly self-misguided. B...
In ordinary set theoretic context, there is no object called 'infinity' that is an operand in an addition operation. Is that supposed to be the lemins...
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