Post AD7oKmzsaqVIeTmL1U by shironeko@fedi.tesaguri.club
(DIR) More posts by shironeko@fedi.tesaguri.club
(DIR) Post #AD7cf6Mr5JVX4QRcxM by Paradox@busshi.moe
2021-11-06T10:56:14Z
1 likes, 1 repeats
Divide by 0 doesn't work because we only defined division with regards to non-zero numbers.Solution: invent a new function that is defined for zero.What actually should happen if we "divide" a number by zero?To elaborate, conceptually, divide by zero works just fine. It would be zero or maybe infinity. There's a few arguments you could make.Technically though, because of its relationship with multiplication, we can't assign a value to n/0 because it wouldn't work with both functions.
(DIR) Post #AD7cjwWT7DS5z7FXai by chjara@mk.absturztau.be
2021-11-06T10:57:07.796Z
1 likes, 0 repeats
@Paradox@busshi.moe in calculus, division by 0 is actually defined in certain cases, as the limit to a function
(DIR) Post #AD7d42f40Ag8oaqzya by newt@stereophonic.space
2021-11-06T11:00:43.728329Z
1 likes, 0 repeats
@chjara @Paradox no, it isn’t. That thing in limit isn’t division by zero.
(DIR) Post #AD7dH829L41lF2tO3U by newt@stereophonic.space
2021-11-06T11:03:05.847958Z
1 likes, 0 repeats
@Paradox you can’t divide by zero because if you then multiply the result of that by zero, you won’t get the original number, silly :comfyjoy:
(DIR) Post #AD7dQBFgk5C3pUXcXo by Paradox@busshi.moe
2021-11-06T11:04:44Z
1 likes, 0 repeats
@chjara Isn't that more an "as this approaches zero"? Like the value converges toward something close to zero but actually at zero it falls apart.They have a word for that point at zero but I forget it.*googles* Discontinuity points.
(DIR) Post #AD7dR8h1k57QBMmmqe by aety@mk.absturztau.be
2021-11-06T10:58:14.347Z
1 likes, 0 repeats
@Paradox@busshi.moe well that's why it's undefined although if we had to assign something i would go for infinity
(DIR) Post #AD7debwUIyd0f7RQNE by Paradox@busshi.moe
2021-11-06T11:07:21Z
1 likes, 0 repeats
@newt Hence the last sentence of my post. Because of that relationship with multiplication, nothing works.
(DIR) Post #AD7drkNEGjgQZmDH4C by newt@stereophonic.space
2021-11-06T11:09:42.839332Z
1 likes, 0 repeats
@Paradox I mean, division is multiplication :comfygeek:
(DIR) Post #AD7eP6FFyM4jxuO6ka by p@freespeechextremist.com
2021-11-06T11:15:48.393715Z
6 likes, 0 repeats
@Paradox FPUs and CPUs have defined division by zero before (and IEEE 754 specifies multiple definitions), not because it's useful to define on its own, but mainly because it keeps the design simple. The issue is "What are you calculating?" Abstract symbol manipulation is fun, but division by zero isn't useful for anything. What would the quantity *mean*?To demonstrate the difference between syntax and semantics, Chomsky constructed this sentence: "Colorless green ideas sleep furiously." Syntactically, it's a perfectly valid sentence, but it doesn't actually mean anything. You could come up with a meaning for it, but there's not much point to doing so.The notations for math that have been created over the years are intended to express some kind of meaning about quantities: we have a meaning for division, but division by zero is meaningless unless there is something you want to express.
(DIR) Post #AD7ffbGyToKsmdchdY by FisaCourtHoarder@social.linux.pizza
2021-11-06T11:29:53Z
1 likes, 0 repeats
@Paradox For ever increasingly small denominators 1/x approaches infinity, and for negative denominators -infinity. This is true for any numerator.Therefor it always made sense to me that division by zero just equals ±∞
(DIR) Post #AD7gZRUU2KCYf4ZNL6 by Paradox@busshi.moe
2021-11-06T11:40:02Z
0 likes, 0 repeats
@newt In a sense. Reverse multiplication.
(DIR) Post #AD7giTGgnTuSmSQGaO by kogomi@void.brechanegra.net
2021-11-06T11:07:10.992486Z
0 likes, 0 repeats
@chjara @Paradox or in the [-inf,+inf] system https://en.m.wikipedia.org/wiki/Extended_real_number_line
(DIR) Post #AD7giTrYaPOscnfi3E by kogomi@void.brechanegra.net
2021-11-06T11:10:41.444640Z
1 likes, 0 repeats
@chjara @Paradox maybe this is more accurate to what I meant https://en.m.wikipedia.org/wiki/Projectively_extended_real_line
(DIR) Post #AD7gjPq91ojWRDSOu0 by Paradox@busshi.moe
2021-11-06T11:41:52Z
0 likes, 0 repeats
@kogomi Really interesting. :o
(DIR) Post #AD7gniv02OGOlamY2S by newt@stereophonic.space
2021-11-06T11:42:35.421257Z
0 likes, 0 repeats
@Paradox no no no. It’s multiplication by the reciprocal. Or at least that’s how fields in algebra are defined.
(DIR) Post #AD7h5wpP3nDH7Sr2CO by Paradox@busshi.moe
2021-11-06T11:45:56Z
1 likes, 0 repeats
@p That is true. Just because you can define something doesn't mean you should, and in most cases if you're hitting a divide by zero exception, you need to rework your process.On the other hand, I'm sure somebody has or will find a good use case for such things, even if it's trivial. May the ideas sleep explosively.
(DIR) Post #AD7hNL0gPClT2cQGRc by Paradox@busshi.moe
2021-11-06T11:49:03Z
0 likes, 0 repeats
@newt I think you're hitting a case of tomayto, tomahto.The idea behind division is you're splitting something into more pieces, while multiplication involves merging multiple pieces into one, the rest is bookkeeping on how many things were needed to make the whole.Also reciprocals involve dividing so it's not like you can define division as pure multiplication.
(DIR) Post #AD7hOf5pDtbJcJSWqO by FisaCourtHoarder@social.linux.pizza
2021-11-06T11:42:26Z
1 likes, 0 repeats
@Paradox I said "This is true for any numerator"I forgot 0. 0 divided by anything is 0.
(DIR) Post #AD7jL2A7i4QHunrqAS by p@freespeechextremist.com
2021-11-06T12:11:05.811651Z
1 likes, 0 repeats
@Paradox Well, I don't know: is there some meaningful concept that we could express if we defined division by zero? Stuff like this has happened, quantum physics uses complex numbers to represent real things ( https://en.wikipedia.org/wiki/Wick_rotation , https://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation ), despite √(-1) being ostensibly meaningless. I'm not sure there will be something we need to communicate that we can communicate by dividing something by zero.
(DIR) Post #AD7jVgNl1nUPYDK33A by newt@stereophonic.space
2021-11-06T12:12:55.010316Z
0 likes, 0 repeats
@Paradox nah, it’s backwards. Division is defined in terms of reciprocals. The latter is just a relation between two elements of a field.
(DIR) Post #AD7oKmzsaqVIeTmL1U by shironeko@fedi.tesaguri.club
2021-11-06T13:07:02.654755Z
3 likes, 1 repeats
@p @Paradox I think plenty of physics use Riemann sphere which defines division by zero
(DIR) Post #AD7q0dYYBTaHULVvsm by p@freespeechextremist.com
2021-11-06T13:25:50.743391Z
3 likes, 0 repeats
@shironeko @Paradox > I think plenty of physics use Riemann sphere which defines division by zero:johnnyrico: [desire to know more intensifies]
(DIR) Post #AD7st3AbMvH4TRO0LQ by shironeko@fedi.tesaguri.club
2021-11-06T13:58:03.485683Z
1 likes, 0 repeats
@p @Paradox just the natural c/0=infinity and such.
(DIR) Post #AD8Y8EW5Yq7u83nLto by NeonPurpleStar@outerheaven.club
2021-11-06T21:40:13.332430Z
3 likes, 0 repeats
@p @Paradox @shironeko Nope, no physics uses the Riemann sphere. I have a master's in general relativity and never had to use it.The thing physicists most often do is taylor expand everything until you get an approximate solution.
(DIR) Post #AD8fEFHUKZL9utmPC4 by shironeko@fedi.tesaguri.club
2021-11-06T22:59:44.246063Z
2 likes, 0 repeats
@NeonPurpleStar @Paradox @p well, idk much physics but from what I've read at least qubits can be represented on a Riemann sphere and it seems to be pretty standard. One can certainly avoid using it I suppose, it's all symbolic most of the time anyway (until it gets down to computers)
(DIR) Post #AD8h4j330DIRFZc68O by NeonPurpleStar@outerheaven.club
2021-11-06T23:20:26.620514Z
2 likes, 1 repeats
@shironeko @Paradox @p That is called the Bloch sphere.https://en.wikipedia.org/wiki/Bloch_sphere
(DIR) Post #AD8hnFl6kKU5RTSFzk by shironeko@fedi.tesaguri.club
2021-11-06T23:28:28.546346Z
2 likes, 0 repeats
@NeonPurpleStar @Paradox @p cool
(DIR) Post #AD8kiKc5ZN9muea58S by NeonPurpleStar@outerheaven.club
2021-11-06T23:38:58.013844Z
0 likes, 0 repeats
Sorry, if it looks like I am trying to come off as smart or anything.In fact I had a lot of trouble preparing for the exams on that stuff and some anxiety from that time is still in me today.
(DIR) Post #AD8kiL6DlLGAQ6g96O by shironeko@fedi.tesaguri.club
2021-11-07T00:01:11.924738Z
0 likes, 0 repeats
@NeonPurpleStar no, no, not at all. they way physics uses math is fascinating to me. physics and statistics actually, to solve a single problem it could be using things from all over math, while when you study math often it's just "let's play with groups today!" or whatever.
(DIR) Post #ADAU4dl1TKgdo77cmG by p@freespeechextremist.com
2021-11-07T20:04:11.564472Z
1 likes, 0 repeats
@shironeko @Paradox I mean why is it that you would need to model that?
(DIR) Post #ADAUAVcQe05wIrttuy by dubh@collapsitarian.io
2021-11-07T20:05:14.202508Z
2 likes, 0 repeats
@p @Paradox @shironeko To find the limit of furious sleeping, duh.
(DIR) Post #ADAX2Izxyxb2hwgqTw by shironeko@fedi.tesaguri.club
2021-11-07T20:37:22.326101Z
2 likes, 0 repeats
@p @Paradox it turns the complex plane into a sphere.
(DIR) Post #ADros5in2tnLbRTFmy by neko@cum.desupost.soy
2021-11-28T17:49:46.540503Z
1 likes, 0 repeats
@Paradox tl;dr ZERO IS A SHITTY FUCKING NUMBER
(DIR) Post #ADrowpfm8q4bHEJzuK by yes@social.handholding.io
2021-11-28T17:50:40.111372Z
0 likes, 0 repeats
@Paradox is this division by zero from the positive side or the negative side?
(DIR) Post #ADrp0ZBJOjYVHvqwdM by Paradox@busshi.moe
2021-11-28T17:51:19Z
1 likes, 0 repeats
@neko XD
(DIR) Post #ADrp63Uu6xFWl9dONM by Paradox@busshi.moe
2021-11-28T17:52:19Z
0 likes, 0 repeats
@yes The positive side, but my argument assumes it doesn't matter.
(DIR) Post #ADrpDX2afUImPhxKfA by yes@social.handholding.io
2021-11-28T17:53:41.233745Z
0 likes, 0 repeats
@Paradox so you turn division by zero function into a kind of atom similar to the imaginary number? if you can find rigor from doing so let us know.
(DIR) Post #AE4czqAT1DwTAaCu5A by CptFabulous@mastodon.social
2021-12-04T22:07:57Z
0 likes, 0 repeats
@Paradox you'd have to preserve the info as to what number was dovided by 0. If x/0 is some constant it would break quite a lot of stuff, like 1 not being 2 -> https://www.math.toronto.edu/mathnet/falseProofs/first1eq2.html That "proof" relies on division by 0.(Spoiler: Step 2^3)
(DIR) Post #AE4d13eAODGLGPgBHs by CptFabulous@mastodon.social
2021-12-04T22:08:12Z
0 likes, 0 repeats
@Paradox you'd have to preserve the info as to what number was divided by 0. If x/0 is some constant it would break quite a lot of stuff, like 1 not being 2 -> https://www.math.toronto.edu/mathnet/falseProofs/first1eq2.html That "proof" relies on division by 0.(Spoiler: Step 2^3)
(DIR) Post #AE4gG5ftQqXBl8LYPo by CptFabulous@mastodon.social
2021-12-04T22:10:00Z
0 likes, 0 repeats
@newt @Paradox wait, possibly stupid question, but if division is multiplication by the reciprocal, how is the reciprocal defined? I thought it'd rely on division(?)
(DIR) Post #AE4gG6DDQxBnQTwAM4 by newt@stereophonic.space
2021-12-04T22:44:23.029265Z
0 likes, 0 repeats
@CptFabulous @Paradox depends on how you think of it. For real numbers, this is kinda the case, but you can also think about division and reciprocity in the opposite way.But you can totally have groups other than numbers that also have reciprocals.Think about reciprocal as an abstraction derived from division, but applicable to other groups in general.
(DIR) Post #AFRh49pL3nBy8gOEIC by FisaCourtHoarder@social.linux.pizza
2022-01-14T21:03:52Z
1 likes, 0 repeats
@Paradox Also while it is "true" for any numerator, it is opposite for negative numerators.Obiously.
(DIR) Post #AFRh4AGdQJ1hVLA1q4 by Paradox@busshi.moe
2022-01-14T23:04:01Z
0 likes, 0 repeats
@FisaCourtHoarder I respect the clarification 70 days later.I'd totally forgotten but I appreciate it.
(DIR) Post #AFRkSeke2H74rTZGPQ by FisaCourtHoarder@social.linux.pizza
2022-01-14T23:42:02Z
0 likes, 0 repeats
@Paradox It was bugging me this whole time because I thought of it later the same day, but...so many people had already interacted with the original so I felt bad deleting and reposting.
(DIR) Post #AFRklRBUhYDcHp58rY by Paradox@busshi.moe
2022-01-14T23:45:28Z
0 likes, 0 repeats
@FisaCourtHoarder I feel that. Thanks. 👍