What is your favorite math constant that is NOT a real number?
a year ago by Ad4mWayn3 to c/asklemmy
You only get NaN for division by zero if you divide 0 by 0 in IEEE floating point. For X/0 with X ≠ 0, you get sign(X)•Inf.
And for real numbers, X/0 has to be left undefined (for all real X) or else the remaining field axioms would allow you to derive yourself into contradictions. (And this extends to complex numbers too.)
ε, the base of the dual numbers.
It’s a nonzero hypercomplex number that squares to zero, enabling automatic differentiation.
Came here to say this, but since it's already here, I'll throw in a bonus mind-melting fact: ε itself has no square root in the dual numbers.
As a not good at math person, advanced math sounds hella fake sometimes. Like almost a parody of math. I accept that it's real but part of me will always think it's some inside joke or a secret society cult for the lamest god.
A lot of "advanced" maths comes from asking "What if this was a thing, how would that work? Would it even work?", so you could say there's a deliberate sense of "fake" about it.
Dual numbers come from "What if there was another number that isn't 0 which when multiplied by itself you get 0?"
Basic dual numbers (and complex numbers) are no harder than basic algebra, shallow end of the pool kind of stuff, but then not everyone is comfortable getting in the water in the first place, and that's OK too.
Thank you for the info!
Puts on floaties and a brave face, then advances to the shallow end
What is the value in learning about "What if there was another number that isn't 0 which when multiplied by itself you get 0?"
Are there any practical applications IRL for dual numbers?
Edit: Screw Screw theory. Wikipedia says dual numbers have applications in mechanics and to see Screw Theory. I tried reading about it and my eyes glazed over so quickly. Math so isn't for me lol.
j = √-1
This comment was sponsored by EE gang
Set phasors to "confuse"
√-4 = 2
It's all fun and games until someone loses an i.
i=sqrt(-1) is nice, but im hoping someone finds a use for the number x where |x| = -1 or some nonsense like that because it looks fun to mess with
Those exist in the split-complex number system which adds the number j, where j^2=1 (but j does not equal 1 or -1). The modulus of j is -1.
I'm a big fan of 10-adics, especially this one.
j is cool too, as is (1+j)/2.
Elevendy
Matrix representations in general, if that counts?
Complex numbers, polynomials, the derivative operator, spinors etc. they're all matrices. Numbers are just shorthand labels for certain classes of matrices, fight me.
I'm just being silly, but I mean that if everything can be represented as a matrix then there's a point of view where things like complex numbers are just "names" of specific matrices and the rules that apply to those "names" are just derived from the relevant matrix operations.
Essentially I'm saying that the normal form is an abstract short hand notation of the matrix representation. The matrices are of course significantly harder and more confusing to work with, but in some cases the richness of that structure is very beautiful and insightful.
(I'm particularly in love with the fact one can derive spinors and their transforms purely from the spacetime/Lorentz transforms. It's a really satisfying exercise and it's some beautiful algebra/group theory.)
I always like seeing π.
Pi written out is a real number, yes, I’m referring to the symbol representing Pi. Does that not count?
Nnnnno.
Chaitin's constants.
Not even a number.
Oops, I misunderstood what an uncomputable is...
In that case, I would say Infinity-Infinity. This time, it's truly not a number.
For a while 1 wasn't considered to be a number either http://aleph0.clarku.edu/...
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Doxxing, trolling, sealioning, racism, toxicity and dog-whistling are not welcomed in AskLemmy. Remember what your mother said: if you can't say something nice, don't say anything at all. In addition, the site-wide Lemmy.world terms of service also apply here. Please familiarize yourself with them
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I have a strong relationship to what you get when you divide by zero.
Good ol' NaN
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