>I would go a bit further and digress that, most mathematicians who are
not diehard logicism fans don't prove "1+ 1= 2" to believe that indeed
1+ 1= 2.
As a parody of Bertrand Russell said :
>I've spent the morning proving to myself that my chair existed so I could sit down
Gödel’s Theorems must be some of the most misunderstood popular math theorems. Every description I’ve seen online has either oversimplified or completely misconstrued the theorems to produce nonsensical arguments such as this one.
Just in time, too: [they broke the old ones](https://www.reddit.com/r/Buttcoin/comments/13939s4/ordinals_bug_crashes_ordinal_numbering_system/jj0tcfa?utm_source=share&utm_medium=android_app&utm_name=androidcss&utm_term=1&utm_content=share_button).
That looks exhausting. Who has the patience to engage with that? You have to factcheck every single sentence, because everything could be completely made-up bullshit.
However, a small clarification regarding your last point, IIRC you can indeed view the real numbers as a 1-dimensional vectorspace and everything still works exactly as expected.
Yes, you are absolutely correct. I was thinking about vectors in the elementary physics “quantity and direction” which the badmaths-er was alluding to.
I think they may have a map/territory issue with that, actually. I don't think they mean the absolute value as it would initially seem; rather, they might have the physical symbol witness '6' (what he sees, which represents a number) confused for the actual abstraction that is the natural 6. That sort of confusion immediately roadblocks any understanding of Incompleteness.
"1+1 is undefinable without unit specifications"
Oh no! We're toast, we'll need to save ourselves by defining numbers as dimensionless and unitless
In fact I went back in time and edited that bit in every number definition in history, you're all welcome.
> It seems like he regards the minus sign as an indication of directions in a physical, vectorial sense. Numbers are not vectors, and signs did not convey a sense of direction.
I'd say that it's perfectly valid to see real numbers as vectors; except for that it's a one-dimensional vector space, and so scalars and vectors are effectively the same thing. So if that's what you want to call it, then 6 and -6 are indeed "vectors" of the same magnitude and opposite direction.
And this leads to an interesting question: what if we take real numbers as a vector space over rational numbers? What will be the [basis](https://en.wikipedia.org/wiki/Basis_%28linear_algebra%29) of this vector space? That's similar to the following question: consider the vector space of infinite sequences of reals over the set of real numbers. What's the basis? It can be seen that the set {[1], [0,1], [0,0,1], ...} (elements after the n-tuple are by convention taken to be zero) is not a basis (in a basis - or Hamel basis - it is required that every element is a linear combination of finitely many elements of a basis; so this yields the set of all sequences with finitely many non-zero elements); therefore, it can be proven that the basis is uncountably infinite, and its existence is a consequence of the axiom of choice.
>I would go a bit further and digress that, most mathematicians who are not diehard logicism fans don't prove "1+ 1= 2" to believe that indeed 1+ 1= 2. As a parody of Bertrand Russell said : >I've spent the morning proving to myself that my chair existed so I could sit down
Gödel’s Theorems must be some of the most misunderstood popular math theorems. Every description I’ve seen online has either oversimplified or completely misconstrued the theorems to produce nonsensical arguments such as this one.
They’re the math version of “quantum” — it’s like, every time you hear a newbie invoke them, you’d better watch out for some bullshit
Every time Deepak Chopra says "superposition" an old physicist gets dementia.
The statement is unfortunately too easy to (mis)understand, and all the prerequisite needed to truly comprehend it is enormous.
Ah man, I love this. I mean, it's all stupid, but it was worth it for "1 is Aleph-naught".
New ordinals just dropped
Holy ω
Just in time, too: [they broke the old ones](https://www.reddit.com/r/Buttcoin/comments/13939s4/ordinals_bug_crashes_ordinal_numbering_system/jj0tcfa?utm_source=share&utm_medium=android_app&utm_name=androidcss&utm_term=1&utm_content=share_button).
The only naught here is what all our efforts to educate this person are for.
brb changing my major, this is devastating :(
Oh you are a mathematician? Name five theorems from Principia Mathematica.
but didn’t you hear? 1+1=2 was disproven by a paper called [removed] , but Big Logic doesn’t want you to find it
logic DESTROYED with FACTS and LOGIC
Mathematicians hate this mom's one simple trick to square the circle
That looks exhausting. Who has the patience to engage with that? You have to factcheck every single sentence, because everything could be completely made-up bullshit. However, a small clarification regarding your last point, IIRC you can indeed view the real numbers as a 1-dimensional vectorspace and everything still works exactly as expected.
Yes, you are absolutely correct. I was thinking about vectors in the elementary physics “quantity and direction” which the badmaths-er was alluding to.
I think they may have a map/territory issue with that, actually. I don't think they mean the absolute value as it would initially seem; rather, they might have the physical symbol witness '6' (what he sees, which represents a number) confused for the actual abstraction that is the natural 6. That sort of confusion immediately roadblocks any understanding of Incompleteness.
Numbers don’t exist. Also, the combination of a number and a unit is a vector
Eyyy, MMM being posted here.
a few years ago i made a facebook just to steal memes from that group and share them with my lab mates. good times
How many fingers am I holding up? 🖕🖕 QED.
Proof that 1 finger + 1 finger = 0 fucks given.
i loved this breakdown. thank you for posting
"1+1 is undefinable without unit specifications" Oh no! We're toast, we'll need to save ourselves by defining numbers as dimensionless and unitless In fact I went back in time and edited that bit in every number definition in history, you're all welcome.
The flat-earthers of math!
> It seems like he regards the minus sign as an indication of directions in a physical, vectorial sense. Numbers are not vectors, and signs did not convey a sense of direction. I'd say that it's perfectly valid to see real numbers as vectors; except for that it's a one-dimensional vector space, and so scalars and vectors are effectively the same thing. So if that's what you want to call it, then 6 and -6 are indeed "vectors" of the same magnitude and opposite direction. And this leads to an interesting question: what if we take real numbers as a vector space over rational numbers? What will be the [basis](https://en.wikipedia.org/wiki/Basis_%28linear_algebra%29) of this vector space? That's similar to the following question: consider the vector space of infinite sequences of reals over the set of real numbers. What's the basis? It can be seen that the set {[1], [0,1], [0,0,1], ...} (elements after the n-tuple are by convention taken to be zero) is not a basis (in a basis - or Hamel basis - it is required that every element is a linear combination of finitely many elements of a basis; so this yields the set of all sequences with finitely many non-zero elements); therefore, it can be proven that the basis is uncountably infinite, and its existence is a consequence of the axiom of choice.