Mariano Wise Words

DanZimm

May 17, 2013 08:02

but my mind is being blown that you can divide by 0

Mariano Suárez-Alvarez

you cannot divide by zero

DanZimm

@GustavoBandeira grants immaturity

Mariano Suárez-Alvarez

if you limit yourself to working with real numbers

DanZimm

then what is happening when 1/0

Mariano Suárez-Alvarez

there is no reason why you should limit yourself to working with real numbers

DanZimm

May 17, 2013 08:03

what numbers is this ok?

Gustavo Bandeira

@DanZimm I noticed it, I just wouldn't starting joking like "Heh! You said ass! Ah hahaha"

DanZimm

:P

Mariano Suárez-Alvarez

if you introduce $\inf5y$ to the real numbers, you get a consisten system with certain limitations

it is no longer a field

for example, with addition, you do not get a group

but you do get something

Gustavo Bandeira

@DanZimm Mathematics does not seem to be a religion, it seems to be more something that we build.

Mariano Suárez-Alvarez

if you are careful when you operate you will be safe

DanZimm

May 17, 2013 08:04

@MarianoSuárez-Alvarez totally forgot about this, I completely apologize about this whole debacle

Mariano Suárez-Alvarez

you are used to numbers commuting, for example: $1\cdot 2=2\cdot 1$

but something syou want things not to commute

not just out of fun but because you need them not to

DanZimm

interesting

Mariano Suárez-Alvarez

Heisenberg invented matrix mechanics that way, for example

(this is one of the ways to decribe quantum mechanics)

you are also used to products being an associative operation

but sometimes you want them not to be

and so on and on and on

DanZimm

hrm interesting

Mariano Suárez-Alvarez

there is no reason to limt yourself t the field of real numbers

DanZimm

May 17, 2013 08:07

yea I was being silly

Mariano Suárez-Alvarez

also, there is great intuitional value in infinite and infinitessmals

DanZimm

yea i agree

Mariano Suárez-Alvarez

(and there are variious ways of making them an actual formal theory, like non-standard arithmetic)

DanZimm

hrm

Mariano Suárez-Alvarez

all this does not imply at all that when physicists write 1/0 = infty they are making sense of course :-0

but they might be

further analysis is required to be sure!

DanZimm

May 17, 2013 08:09

but based on the real line with traditional arithmetic, that statement doesnt make sense

and heh yea

Mariano Suárez-Alvarez

you are committing the sin of adscribing to others limitations of yours

why are you assuming they are bounding themselves to operate within the field of real numbers?

DanZimm

im saying if one does only look at the real numbers

Mariano Suárez-Alvarez

(even if they do think they are operating with th field of real numbers :-) )

DanZimm

im not talking about physicists at all anymore

and with traditional arithmetic?

skullpatrol

What does "=" mean in this context?

Mariano Suárez-Alvarez

May 17, 2013 08:11

well, in the theory of peano arithmetic there is no -1

let alone $\infty$ :-)

DanZimm

the traditional equality, considering I'm talking about if someone is using the traditional idea of arithmetic

again, not peano

Mariano Suárez-Alvarez

equality is just equality

you are mixing things

Dominic Michaelis

There is no problem dividing by zero, just take the ring over $\{0\}$ we can define $ 0 *0=0 $ and $0+0=0$ and hence $0/0=0$

Mariano Suárez-Alvarez

there is no problem dividing by zero if you are ok with not having a field

just as there is no problem with non-commutative division algebras which are fields in which commutativity does not hold

Dominic Michaelis

I am born in the city i don't need fields :D

Mariano Suárez-Alvarez

May 17, 2013 08:13

there is no rule that we have to work with fields

DanZimm

but if youre working with the real numbers (meaning a field) then 1/0 = inf doesnt make sense, right?

Mariano Suárez-Alvarez

we work with whatever is convenient to do what we want

@DanZimm of course

no one is saying it does

DanZimm

well jesus thats all i was trying to clarify xD

Dominic Michaelis

@DanZimm but it even doesn't makes to calculate with fractions if you are in the natural numbers

Mariano Suárez-Alvarez

well, that is sort of a silly thing to try to clarity

1/0 simply does not make sense

it cannot be equal to anything

skullpatrol

May 17, 2013 08:15

Does $\infty=\infty$?

Mariano Suárez-Alvarez

included infinity

infinity is nothing

it is not a real number

Gustavo Bandeira

@MarianoSuárez-Alvarez It is something on non-standard analysis, right?

Like surreal numbers, I guess.

DanZimm

@MarianoSuárez-Alvarez yea thats what i was just clarifying meaning i thought you were saying otherwise at first but you werent ergo i was making a bad assumption and so i need to clarify this was the case

Mariano Suárez-Alvarez

if you put yourself in a context in wich infinity is something, then of course it is equal to itself.

Dominic Michaelis

no it is the one point compactifictaion of the real numbers

DanZimm

May 17, 2013 08:16

sometimes im silly :P

@DominicMichaelis who said im talking about the natural numbers lol

Mariano Suárez-Alvarez

@DanZimm the problem with $1/0=infty$ in the context of the field of real nmbers is twofold

theleft hand side does not mean anything, is simply undefined

the right hand side is not a real number

DanZimm

ya i unerstand that

i actualy said that aboove

Mariano Suárez-Alvarez

therefore wondering if the equality holds or not in the context of real numbers is rather weird

Dominic Michaelis

@DanZimm no it was an analogy. For you it absoutly makes no sense throwing away the real numbers to take something different. but Some time ago (about cantor) the real numbers was a very silly concept too

Mariano Suárez-Alvarez

the answer is MU

skullpatrol

May 17, 2013 08:18

So why try and fool everybody and use the "=" sign?

Mariano Suárez-Alvarez

huh?

skullpatrol

2 mins ago, by Mariano Suárez-Alvarez

@DanZimm the problem with $1/0=infty$ in the context of the field of real nmbers is twofold

Here^

Dominic Michaelis

@Danzimm i mean numbers which are no fractions seems kind of weired too doesn't it ?

Mariano Suárez-Alvarez

in a context where both sides of an equality make sense, it of course makes sense to write the equality

DanZimm

@DominicMichaelis right but I was specifically talking about if someone is trying to work with just the real numbers, possibly because theyre ignorant and dont understand these math ideas, which occurs often to many undergrad physics majors

Mariano Suárez-Alvarez

May 17, 2013 08:19

the set $\mathbb R\cup\{\infty\}$ can be endowed with partiaal operations of sum, difference and so on

and there you can operate with care

and there $\infty=1/0$ is a perfectly correct statement, and a true one to boot

that set is certainly not a field, let alone not the field of real numbers

Dominic Michaelis

you don't have to go that far. I tried to convince my theoretical physics prof, that the standard scalar product on $\mathbb{C}$ is not antisymmetric but hermitien, I failed ...

DanZimm

yea

thats i guess why i made any statement originally, i often see people around me studying physics to make some pretty bad assumptions, but it wsa improper of me to generalize that to physicists in general

Mariano Suárez-Alvarez

when one iss working with measure theory, and the correspondding integration theory (Lebesgue and friends) one works with $\infty$ as an actual value all the time; there one only adds those things, not multiply them

actually, with $+\infty$ and $-\infty$

DanZimm

@MarianoSuárez-Alvarez I'm confused as to what you're addressing right now

Mariano Suárez-Alvarez

and you have to be careful when you operate because some things are left undefined, line $\infty-\infty$

I am elaborating my point

DanZimm

May 17, 2013 08:25

which one?

Mariano Suárez-Alvarez

tht you should be more lenient to what the physicists do, because often your discomfort is only indicative of your not knowing what they are doing :-)

DanZimm

because the one with regard to infinity I admited I was wrong on and understand that I'm too ignorant to make such assertings

^

Mariano Suárez-Alvarez

if you think I am writing to chastise you for your mistake, you are wrong

i was hoping to explain the point

as you apparently do not care for that, I'll go do something else

DanZimm

im actually interested, just wanted to make sure you werent chastising ;)

@MarianoSuárez-Alvarez ^

$Mathematics$ Mathematics

Participants