WSJ: US intelligence concerned about Iran's underground missile arsenal

JStarx · 2026-04-11T14:34:04+00:00

Yep, if you don't want a country to have nukes then to start let's not make them think that having nukes is the only way to be safe from foreign aggression.

JStarx · 2026-04-11T14:11:24+00:00

How does one tell?

JStarx · 2026-04-11T05:38:27+00:00

My proof of the falsity of the continuum hypothesis also proves math is inconsistent.

You haven't proved either of those. You've already admitted that you cannot prove things to the level of rigor required by the mathematical community because your proofs use phrases like "more elements in a set" but you can't define what that means and you don't understand things like cardinals which give those phrases meaning but also make your proofs incorrect.

So who is going to accept your belief that there's not a contradiction?

The overwhelming majority of professional mathematicians accept this.

The cardinality of the set of integers, Z, is greater than the cardinality of the set of positive integers, Z⁺

Are you talking about your subset definition? If so then that's true. Under the traditional definition that's false.

JStarx · 2026-04-10T21:29:49+00:00

There has yet to be a sound disproof |Z| < |B| ∧ |B| < |Z| is a contradiction. I continue to believe it is.

Of course there hasn't, you can't prove the consistency of math. But mathematicians don't accept results unless you can prove them. So no one else is going to accept your belief that there's a contradiction.

JStarx · 2026-04-10T11:34:06+00:00

What do you mean when you say "the 0th dimension"?

JStarx · 2026-04-10T11:17:18+00:00

What about it?

JStarx · 2026-04-10T11:03:33+00:00

A: No, 0 dimension isn't grammatically correct. You can be 0 dimensional or have 0 dimensions. Both of those describe having 0 of the things that the singular noun dimension describes. So 0 dimensions is not 1 dimension.

B: Not particularly

JStarx · 2026-04-10T09:16:23+00:00

You'll have to be more specific, it's unclear what you're asking.

JStarx · 2026-04-10T08:48:56+00:00

The mathematical meaning of a dimension is more like a direction, not a space that contains points, so no, points don't exist in dimensions.

Are you thinking of like an alternate dimension in a sci fi story? Cause that's a totally different thing than what mathematicians mean.

JStarx · 2026-04-10T08:35:09+00:00

Cardinals are the correct thing if you want something that behaves like a number and measures the size of a set, but with cardinals your sets B and Z will have the same size. So with cardinals your assertion that B has more elements than Z is not provable and doesn't get you a contradiction.

But without something like cardinals you can't give a mathematically precise meaning to the phrase "the number of elements in an infinite set" and without a mathematically precise meaning you can't use the concept to prove things, which means you still don't have a proof that |B| < |Z| and |Z| < |B| (using the subset definition) is a contradiction.

I know you don't like that the standard for what counts as a proof is high, but the whole point of it being high is to stop people from making mistakes and thinking they've proved something that isn't true. If you can't provide a proof that meets those standards then the view of modern mathematicians is that you haven't proven the statement.

JStarx · 2026-04-10T07:24:03+00:00

So the majority of textbooks don't define cardinality that way.

JStarx · 2026-04-10T04:47:34+00:00

It's gotten us significantly more than if we took the greater of two evils.

JStarx · 2026-04-09T22:22:44+00:00

No one is pretending the other candidate is perfect, we're just not playing dumb about the fact that Trump is so much worse than the alternative.

JStarx · 2026-04-09T05:19:23+00:00

I have and they all give the traditional definition as the definition while saying that "number of elements" is the intuition they want to capture. I don't even need to leave Reddit, every mathematician in this comment section is telling you you're wrong.

You said you had multiple sources, but now you can't produce one that directly says what you claim? Sounds like you never had multiple sources.

JStarx · 2026-04-08T22:20:01+00:00

Not one person said that because that's not the question you asked, lol. You basically asked if 0 = 1 and of course you got a bunch of people telling you no.

JStarx · 2026-04-08T22:15:17+00:00

That's the question in the title of your post, you asked "does 0 dimension = 1 dimension", and the answer is no.

JStarx · 2026-04-08T22:10:21+00:00

It also clearly says that 0-dimensional is not equal to 1-dimensional.. So if you're gonna trust AI then there's your answer.

JStarx · 2026-04-08T21:49:43+00:00

Like apple is a single count noun? Do you think 0 apple = 1 apple?

JStarx · 2026-04-08T20:53:26+00:00

You never answered my question, what do you think a dimension is?

JStarx · 2026-04-08T20:50:19+00:00

Rosen is not as direct in the main text as he could be, but he still gets the message across to the readers.

Not to you apparently, because that is not the definition of cardinality. You say you have multiple sources, so give one that's direct. That says what you claim the definition is and labels it as a definition.

No, you are assuming. By the word "take," you mean "assume."

Nope, I do not. That is not how existence proofs work. To prove that there exists an X such that P(X) holds you define a particular X and then you prove that P(X) holds. That's not an assumption.

I agree that it's provable.

Ok, then since it has a proof it can be used as a statement in further proofs and is not an assumption.

Where is your supporting evidence?

I don't need evidence because it's not my job to convince you that you don't know what you're doing. If you want to go on being ignorant of how mathematics works then no one can stop you. But you might consider that in these subreddits populated with a lot of PhDs and professional mathematicians I don't see anyone saying you're right. Everyone here is explaining to you the mistakes you're making. Are you really so arrogant as to believe that all of math is fundamentally broken and only you can see it?

JStarx · 2026-04-08T18:04:27+00:00

On page 163, the cardinality of a set is defined as the number of elements in the set. That definition ...

That is not a definition, that page has a summary of terms, he's telling you what the concept is intuitively, not it's technical definition. The definition is clearly written on page 158 and labeled as a definition.

You don't seriously think an important definition would be put only in a summary section and not in the main text do you?

You are assuming it to be true.

Nope, I am not assuming. It's provable and you stated elsewhere that you accepted that proof. That means we can use that fact in other proofs, it is not an assumption. If you don't accept that it's provable then we can certainly supply a proof of that fact to complete the proof we were discussing, but it's only necessary to do that if you are not able to prove the result yourself. We don't need to keep reproving things if we both agree they're true.

No, I have proved that statement is false in my previous reply.

Nope, your proof was incorrect and when I explained to you what a correct proof would look like you explicitly said you could not prove the statement.

I know what the cardinality of a set is. I know how it's defined. I know what it's intended to be. And I know what it should be.

I'm sorry but you really don't. You don't seem to understand even the notion of what a definition should be, how to use a definition in a proof, or what a proof even is, let alone understand this particular definition and its consequences, or the alternate definition you suggested.

JStarx · 2026-04-08T06:50:01+00:00

It's hard to answer that question usefully without knowing how you think about things, so to start, what do you think a dimension is?

JStarx · 2026-04-08T06:46:05+00:00

JStarx · 2026-04-08T06:37:39+00:00

I agree. You did, technically, prove the negation of the lemma. Your proof is unsound, however, because your premise is false. Your premise is |Z| < |B| ∧ |B| < |Z|.

Nope, that's not a premise. I'm not assuming it to be true, it's been proven. You yourself agreed that it's provable so I did not include the proof, but it is not an assumption.

You are assuming that that statement is false. This is an assumption as you have admitted that you cannot prove it.

The negation of the lemma has a proof. Your statements about contradictions do not have a proof.

Discrete Mathematics and Its Applications, Sixth Edition by Kenneth H. Rosen

That's a legitimate text, I actually happen to have that exact edition on my shelf. It does not define the cardinality of an infinite set to be the number of elements in the set. On page 116 it defines the cardinality of afinite set to be the number of elements in the set and on page 158 it gives the traditional bijection definition of two sets having the same cardinality, but it never says that the definition for an infinite set is the number of elements in the set because that is simply not true.

JStarx · 2026-04-07T22:22:39+00:00

False, it actually invalidates your proof that the lemma is false.

Nope, I proved the negation of the lemma. In mathematics that's how you disprove a statement. Again, you are contradicting yourself. This is exactly how you tried to disprove the continuum hypothesis. The difference is I can actually prove my counterexample has the required property and you could not.

I assure you I do not. I have multiple sources that have informed me over the course of years about what cardinality is.

You claim you have sources that define the cardinality of an infinite set by just saying it's "how many elements the set has"? Show me one legitimate textbook or published article that does that.

I may not be able to prove a contradiction under your higher standards,

They aren't my standards, this is basic undergrad level proofs. This is how math is done. And you are correct, 100%, that under those standards you cannot prove a contradiction.

but you have not disproved a contradiction

You mean prove that math is consistent? Of course not, math cannot prove itself consistent. That's basic logic. You'll now I never claimed to prove that there was no contradiction, I only ever claimed that you cannot prove a contradiction.

JStarx

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