It may be represented that way, but they are not the same thing.
4 and 0 are equivalent as representants of the residue class. If you can write down 2+2 where 2 refers to a residue class, the answer can be written down as 4.
your claim that 4 (sa) = 0 (mod 4)
How many times do I have to ask you to stop misquoting me?
Voyager
1yr ago
you argued that (2+2=4) is always standard arithmetic
No, I didn't. If you believe otherwise, cite where I said it. Or stop misrepresenting me.
As I pointed out numerous times, by 2+2=4 in this context you meant in standard arithmetic
So you're "pointing out" to me what I meant. Have you considered that I can read my mind better than you can? After all, when someone talks about your position elsewhere , you're quick to call it out as assumptions. And when I offer clarification, you ignore it, only to repeat your strawman two posts later.
Obviously I meant "with unspecified context", because that was the example we were talking about. Yes, people don't know you're sneakily talking about modular arithmetic - but "2+2=4" is still true, so people are giving the correct answer, despite the confusion.
That was my clarification. I've had a lot of patience with you, but I can't really have a discussion with someone who talks to their own caricature of me and ignores what I actually say.
if 99.9999% of people think (2+2=4 in standard arithmetic) that does not equate to 99.9999% people thinking (2+2=4 (mod 4))
You weren't asking about 2+2 (mod 4) though. You were asking "2+2=" without context, and people answer "4", which is correct.
If they interpret the meaning of the string "2+2=" different than you, that's not anyone being wrong, that's just a misunderstanding caused by your bad communication. But luckily the misunderstanding doesn't matter, because the answer is correct in either interpretation.
You cut out the part where you specified (2+2=4) in standard arithmetic before I answered. That's the misrepresentation.
Since you seem to have hard time understanding context, I'll repeat my actual statement with the context explicit:
(2+2=4 in standard arithmetic) and (2+2=0 (mod 4)) are not the same statement.
With that cleared up, any further questions?
Voyager
1yr ago
you clearly implied that "more than 0.0001% people think 2+2 is necessarily 4", obviously you meant in standard arithmetic, since very few people know that 2+2=4 (mod 4) even exists.
Obviously I meant "with unspecified context", because that was the example we were talking about. Yes, people don't know you're sneakily talking about modular arithmetic - but "2+2=4" is still true, so people are giving the correct answer, despite the confusion.
And you also accepted 2+2=4 (mod 4) is not the same statement as 2+2=4
Can you just fucking stop misrepresenting me? That would be great, thanks.
Voyager
1yr ago
You are trying to distract from what you said
No, I'm trying to explain what I said, because you keep removing the context:
- 2+2=0 (mod4) is not the same statement as 2+2=0
I said 2+2=4 in standard arithmetic is not the same statement as 2+2=0 (mod 4). I insisted on making this explicit, because it came up on the context of mod 4. And because I suspected you were trying lead me to a contradiction, so I made sure to speak clearly, proofing myself against it.
So if you cut out the important context, and then try to construct a contradiction that doesn't work with the context included, you're misrepresenting me.
Retract and apologize.
(Assuming here you meant to write 4 instead of 0, but otherwise it would just be an even worse misquote, so I'm charitably assuming it's a typo.)
But it's pretty clear that you meant 2+2=4, not 2+2=4 (mod 4), because the former is what most people think is true.
I meant "2+2=4", "in Z/4Z" omitted, as in your original setup*. When it's about people's reaction to the statement, formulation is important.
*But in my case it was available from context, whereas in your example it was deliberate misdirection.
People think it's true, while they're denied the context. But given the full context, which changes the meaning, it's still true.
It's also quite peculiar that you're doing what you're accusing me of: I pointed out you were contradicting yourself, you tried to weasel away, and when I nailed you down, you tried to ignore it. Do you stand by the statement
(2+2=4 (mod 4)) exists, which is not the same as (2+2=4), and you finally accept that they are two different things.
?
Voyager
1yr ago
No, I said (2+2=4 (mod 4)) might not be the same as (2+2=4). I very clearly never said what you claim I'm supposedly "now saying": I said "might not be", never said "is not".
You also said
(2+2=4 (mod 4)) exists, which is not the same as (2+2=4)
So yes, you said it. Do you want to retract that statement now?
YOU claimed (2+2=4) is just another representation of (2+2=0 (mod 4))...
I claimed that 2+2=4 (mod 4) is another representation of 2+2=0 (mod 4). I specified "in Z/4Z" the first time I made my statement, I referred to modular arithmetic the second time, I clarified my statement to the literal same when you asked.
The question I answered referred to 2+2=4 in standard arithmetic(although it took you 5 comments to finally clarify your ambiguous question), which makes it a different question with a different answer.
You're trying to cut out the context, which makes it a misrepresentation of me. Retract and apologize.
(2+2=4 (mod 4)) might be the same statement as (2+2=0 (mod 4)), but not (2+2=4).
So you're now saying that 2+2=4 without further context is not the same statement as 2+2=4 (mod 4)?
Dare I hope you finally saw reason? That you accept that you are not allowed to say "2+2=4" without context and pretend you mean modular arithmetic, and that "2+2=4" is simply true?
(And if you're just going to say the () change the meaning, then you should start off defining your idiosyncratic notation, and by "start off" I mean you should have done it 10 posts ago when you first used it. And then you should retract your argument, since it's a non-sequitur obfuscated by misleading notation.)
Voyager
1yr ago
Really? Wasn't your entire argument relying on the fact that if the arithmetic wasn't specifically specified, then certain arithmetic was always assumed?
It has been specified beforehand:
in Z/4Z, 2+2=0 and 2+2=4 are the same statement.
If in response you talk about standard arithmetic without clearly denoting it, that's just you communicating badly again, which is why I made you add a clarification.
For the record, when I ask ChatGPT if it's always necessarily the case, it answers "no". It says that's not the case in other arithmetics. Weird that it interprets math like me, not like you.
You can get ChatGPT to tell you all sorts of bullshit, including self-contradictions. It's not an authority for anything.
it's standard arithmetic
That makes it a derail, since we were talking about modular arithmetics. But just for the record, the answer is no then.
Voyager
1yr ago
It hurts Germany because it stops them from trading with Russia. But it also distances Germany from Russia, and removes leverage Russia has over Germany.
The US isn't primarily interested in Germany's prosperity - only the political effect thereof. A weakened Germany that is firmly on the side of NATO is better for the US than a prosperous Germany that peacefully trades with Russia and doesn't do anything against them.
Voyager
1yr ago
It's a badly posed question because it's not fully specified, namely, you're not stating where (2+2=4) lives.
Normally this wouldn't be a problem, because we can assume it's the default if not otherwise noted, but a) we'e explicitly discussing multiple number systems here and b) you have already proven you can't be trusted not to omit relevant information.
Your question is ambiguously stated. Normally it wouldn't be, but have earned a reputation of communicating badly. Define whether (2+2=4) in your question is integer arithmetics or (mod 4) (or something else) and I'll answer your question.
Voyager
1yr ago
It's a badly posed question. You have been weaponizing ambiguity the whole time, I'm not accepting your framework without adding context.
If you want a question answered, state it clearly.
Voyager
1yr ago
The OP was definitely talking about "all female or all-Latino trading firms."
OP was talking about undervalued people making their own company. They're all female/minority because that's the reason they're undervalued.
That ain’t happening without selection pressure.
If women are as undervalued as is claimed, the best candidate for a given budget and the cheapest candidate of a given quality will pretty much always be a women. So you don't have commit to only hiring women to end up with all women - it's a natural consequence of optimal behaviour.
Likewise, the “Progressive half” of retail investors would be leaving money on the table if they opted out of the vast majority of the market.
Investors are always opting out of a majority of the market they consider less profitable - profitability just usually isn't as clearly demarcated. The point is that if the claim is true, everyone else is leaving money on the table - so the rational move is to go to the part of the table where the money is lying and pick it up.
Even if you're right, that's a nitpick towards the OP, not a rebuttal. There's still money to be made if you let in the occasional white male who doesn't want more money than he's worth.
Voyager
1yr ago
“African and/or female investors” have no reason to assume the gains from less-biased hiring outweigh the costs of running a business on idpol.
You don't need to "run on idpol". You can just keep in mind that everyone else undervalues the group, then hire purely on cost/quality, and you'll still end up ahead.
Also you're assuming running on idpol has net costs - in the current environment it seems like it has serious marketing advantages.
Voyager
1yr ago
Then you'll still get a decent team for much cheaper than usual, and you can used the saved money to get an advantage in other ways or collect the difference in profit.
Voyager
1yr ago
There is nothing to interpret, it's straightforward math. I'm merely writing it down.
Voyager
1yr ago
I took the liberty of clarifying my position instead of answering the badly posed question. Naturally modular arithmetics is not the same as integer arithmetics.
"2+2=4" is true in both, only in one 2+2=0 is also true.
Voyager
1yr ago
No, math is abstract truth. If the application ever becomes an issue, you're looking to apply math to another field.
In any case, the statement in question is a straightforward arithmetic equation. There's no room for interpretation here.
Voyager
1yr ago
(2+2=4 (mod 4)) and (2+2=0 (mod 4)) is the same statement. If you omit the (mod 4) part, you're merely communicating badly. Again.
Voyager
1yr ago
Slytherins aren't living in squalor - the dungeon ambience is merely an aesthetic.
I have never heard of a "wealthy villains living in squalor" trope, and I struggle to come up with examples.
Also, even if a trope was originally based in antisemitism, if it since has entered the cultural background, and no longer has a connection to jews, because most people are no longer aware of the origin and it doesn't match their own image of jews, then I'd say it's not antisemitic anymore.
Voyager
1yr ago
I'm not ignoring it, I'm rejecting it has any relevance. Everyone doesn't know a lot of things. This is hardly new or interesting.
But the existence of modular arithmetics doesn't make 2+2=4 incorrect. It merely makes 2+2=0 another representation of the same statement. So "most people" remain correct.
Voyager
1yr ago
Then explain how that's supposed to be a response to my point, please.
My point being that in Z/4Z, 2+2=0 and 2+2=4 are the same statement. Ergo, 2+2=0 is merely another way to write down what we think. We might not literally think it, but we are thinking an equivalent statement.
Voyager
1yr ago
And who decides the correctness of my position?
The correctness of your position is a matter of fact. No one decides it, we research it. I have done so and found out it's not correct. If I happened to be wrong about that, there would be convincing counterarguments you could make, proving me wrong. But I notice you're not even trying to argue X anymore.
How is this not the definition of circular reasoning?
It's the definition of a strawman. I have not made the circle of reasoning you describe. I have proven that X is not true, separately.
As the user in question, I can clear this up: Although I didn't make this clear at the time*, I was referring to the statement "2+2=/=4 (mod 4)" (which was @felipec 's argument in favor of "2 + 2 = 4 is not unequivocally true").
This is a plain mathematical statement which I disproved (I didn't publish the formal proof because I wasn't challenged on the informal rebuttal). I consider mathematical proof adequate justification for certainty.
*Perhaps this led to confusion, I might revisit the thread with that in mind.
Notably, this is not the case, the argument in the original post was flawed and the example does not demonstrate what it was supposed to. I had pointed this out in another comment thread and referred to it.
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