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6/24/2025, 12:50:38 AM
>Any of you morons wanna explain why you believe on faith that empty sets are instnatiable objects inside any symbolic manifold?
Hi, moron here. First of all, you misspelled instantiable. Secondly, one does not believe on faith. Faith is belief without evidence. The phrase "believe on belief without evidence (faith)" is nonsensical. Despite this I believe I understand what you meant, right up to the phrase "symbolic manifold". There is something called a symplectic manifold, and you may do numerical calculations on something in a topological space such as a manifold, as opposed to with mathematical expressions, i.e. algebraically, but it rather seems to me you are mixing up terms from computer science and algebra here.
>Literally nothing in the universe behaves that way.
Plenty of things in the universe can behave as if they are empty. On the largest scale we have the cosmic voids, containing barely any or indeed no galaxies, and on the smallest scale the space between an atom's nucleus and its electrons.
Now, before you object, even without mathematical training you should be able to intuit that the empty set captures the idea of emptiness, i.e. the state of containing nothing. Nothing is a word, a semantic construct not without context. If in casual conversation, I say a room is empty, I most certainly do not mean it is somehow in true vacuum, and I have exhaustively checked that there are no particles there, no radio waves going through it, and so on, but rather that there is no furniture there. But to make such an idea of nothing precise, we turn to systems of logic, such as mathematics, with their rigid definitons. An empty set indeed is a set that contains nothing. And not nothing as in a thing labeled nothing, but no things at all: zero members.
>As a hypothesis, it's as empirically justified as the tooth fairy.
Irrelevant, mathematical definitions do not require empirical justification. This is a crucial aspect of math, separating it from the sciences.
Hi, moron here. First of all, you misspelled instantiable. Secondly, one does not believe on faith. Faith is belief without evidence. The phrase "believe on belief without evidence (faith)" is nonsensical. Despite this I believe I understand what you meant, right up to the phrase "symbolic manifold". There is something called a symplectic manifold, and you may do numerical calculations on something in a topological space such as a manifold, as opposed to with mathematical expressions, i.e. algebraically, but it rather seems to me you are mixing up terms from computer science and algebra here.
>Literally nothing in the universe behaves that way.
Plenty of things in the universe can behave as if they are empty. On the largest scale we have the cosmic voids, containing barely any or indeed no galaxies, and on the smallest scale the space between an atom's nucleus and its electrons.
Now, before you object, even without mathematical training you should be able to intuit that the empty set captures the idea of emptiness, i.e. the state of containing nothing. Nothing is a word, a semantic construct not without context. If in casual conversation, I say a room is empty, I most certainly do not mean it is somehow in true vacuum, and I have exhaustively checked that there are no particles there, no radio waves going through it, and so on, but rather that there is no furniture there. But to make such an idea of nothing precise, we turn to systems of logic, such as mathematics, with their rigid definitons. An empty set indeed is a set that contains nothing. And not nothing as in a thing labeled nothing, but no things at all: zero members.
>As a hypothesis, it's as empirically justified as the tooth fairy.
Irrelevant, mathematical definitions do not require empirical justification. This is a crucial aspect of math, separating it from the sciences.
6/22/2025, 5:06:33 PM
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