In the order of operations what comes first, multiplication or division? Addition or subtraction?
>>7702381
I am having trouble thinking of of situations where it would matter, unless you are worried about overflow.
>>7702382
hmm, I suppose you're right.
Jesus, I used to be good at math once, seriously.
what is overflow, mathematically speaking?
>>7702382
111/3(37) = ?
>>7702425
Why not just avoid ambiguity and write it vertically or include more bracketing?
>>7702382
Consider the following posers, which are to be evaluated:
[math] 18 \div 3 \times 2[/math]
[math] 5 - 2 + 1 [/math]
One could perhaps (partly?) rephrase these complementary operations in terms of their inverses (and thereby invoke their appropriate associativity, commutativity etc with respect to one operation), but in a sense this misses the point. What we actually do, in practice, is to learn how to phrase expressions in such a way that context is unambiguous; the stuff of b-tier trolling, however, still actually has (surprisingly) some actual /mathematical/ (and not merely book-keeping) content: /what operation should we do first?/
For example, by an expression such as (the former)
[math] \displaystyle \frac{1+2}{99+ab} [/math]
[math] (1+2) \div (99+(a \times b)) [/math]
, what is really encoded by means of learned context, is the latter more explicit rendering, where OP's question becomes moot in this case if one simply uses brackets.
I am aware of two conventions which are taught to schoolchildren: "PEMDAS" (parentheses, exponentiation, multiplication, division, addition, subtraction), and "BEDMAS" (brackets [parentheses], exponentiation, division, multiplication, addition, subtraction). In each case, the mnemonic is meant to indicate an order or precedence of operations, but this becomes squishy among the operations which invert each other - note the significant interchange of "D" and "M" in the two conventions.
I actually haven't thought this all the way through, but the simplest answer to OP's question is 1) "add more brackets if needed", or 2) "invert operation if needed".
>>7702426
why not answer the question? those are conventional mathematical symbols; does the problem not have a conventional answer?
it's like 1/0 = infinity only when you approach 0 from the positive side? but it's "undefined" because negative infinity is an impossible abstraction
or, perhaps division comes first, since it does when we write it vertically. we do know the answer; we can't approach from negative land because negative infinity doesn't exist. positive infinity does. 1's on top.
>>7702430
*multiplication comes first, rather, when you write it vertically.
>>7702430
Because this is something you never see in uni level maths where we define everything carefully and try to leave as little ambiguity as possible.
When you go into your first year, you'll most likely first see / in the context of quotient groups.
If you write things ambiguously on purpose where the answer varies with the convention of the reader, then you can't really expect anything constructive to arise.
>it's like 1/0 = infinity only when you approach 0 from the positive side? but it's "undefined" because negative infinity is an impossible abstraction
1/x is undefined at 0 yes, but negative infinity most definitely does exist in the same sense as positive infinity does.
The limit from the left side is negative infinity and the limit from the right side is positive infinity.
>>7702414
I'm pretty sure they're talking about programming
>>7702382
2 * 2 + 1 = 5
2 * (2 + 1) = 6
>>7702381
niether, mathematical expressions are written unambiguously, we have brackets and fractions
>>7702469
I was asking about theory; the problem was unimportant
>When you go into your first year
I'm not in school
>but negative infinity most definitely does exist in the same sense as positive infinity does.
not really tho. "negative infinity" is just an abstraction within the realm of actual positive infinity
and again, how can you say 111/3(37) is "ambiguous" if 111 with a flat line underneath it with 3(37) on bottom is unambiguous, if / and - are mathematically equivalent symbols of division?
>>7702481
addition is clearly subordinate to multiplication; however, that wasn't the question.
>>7702382
>>7702414
on the other hand, you're right to object, because the order with division/multiplication also makes a difference; see >>7702425
--
another question. if we have decided multiplication goes first, what bout when it's all division?
333 divided by 3 divided by 3 = ?
left to right or right to left? does the = sign on the right imply left to right?
>>7702502
>I'm not in school
Giving up here anon, good luck to the others who will need to dig deeper to help you understand.
>>7702430
>but it's "undefined" because negative infinity is an impossible abstraction
what the hell are you talking about? you realize all numbers are abstractions, right? Do you know what set theory is?
>>7702425
37(111)/3
>>7702502
>I'm not in school
What's your level of mathematical competency?
>>7702520
like "negative infinity" is a subset of actual infinity
in any case, whether positive infinity or negative infinity, it's still infinity
in other words, the answer is much more discrete than simply "undefined"
>>7702550
>like "negative infinity" is a subset of actual infinity
>subset
>actual infinity
people like this exist?
>>7702558
my 1st cousin teaches math at MIT
and Einstein, himself, said that intuition is the root of all [mathematical] understanding;
https://en.wikiquote.org/wiki/Physics#/media/File:Optical-dispersion.png
>>7702558
He's now speaking in mystical vagaries (encouraged by another anon), because he doesn't actually understand what he's talking about where infinity is concerned (maybe uneducated, maybe troll, but not necessarily stupid). But his original question is still a semantically and mathematically valid one, regardless of its tired status as a b-tier troll (which is exactly what causes math people to dismiss it as trolling, frustration, crankery).
You can build and figure out a system in which of DM or AS you want to go "first", absent any parentheses. See my above post for suggestions.
>>7702584
I'm talking about your formal level of education.
>No, I haven't.
>like "negative infinity" is a subset of actual infinity
How can a single element be a subset of a single different element?
>Otherwise you wouldn't be talking about the problems in the 3rd person
Am I?
>You've left the field
http://www2.warwick.ac.uk/
Try again.
Like some anon before, I'm out of this thread. Trying to deal with you is too annoying.
Good luck to the rest.
>>7702593
>I'm talking about your formal level of education.
I stopped paying attention in math class my junior year in high school (trig). I've since taught myself enough calculus, etc. to satisfy my curiosity/understanding, etc.
I was sleeping through a lot of classes and missing a lot of school, because at that point I was more interested in chess (staying up late at night playing games on the internets). won the high school state championship tho
>How can a single element be a subset of a single different element?
infinity is everything. the technical abstraction that is "negative infinity" - it's just an idea. You can imagine yourself as a hippopotamus too.
>http://www2.warwick.ac.uk/
the battlefield, lulz, not the mathematical field. how autistic are you?
Jeans christ people. The Multiplication and Division are interchangeable. From left to right, do what comes first
>>7702381
subtraction and division don't really exit, so you're not really asking a question
>>7702513
Left to right unless otherwise broken up with brackets.
>>7703155
nah dawg, I before E except after C
it's the first rule of sCIEnce
if you don't follow the rules they taught you in 7th grade, you will never succeed
>>7703155
Barring parenthesises or brackets, division always come first. No matter its position.
honestly why were the order of operations ecen invented
left to right + brackets is all you need
>>7702381
/Not trolling
It depends on which answer you want/need
/not trolling
Is that a scallop? What a beautiful picture.
>>7705143
>scallop
Oh jeez, I just saw the file name. I'll see myself out.
>>7703591
no
4 + 7 x 8 = 60
by your logic it would = 88
>>7703588
see>>7702502
>>7702502
>>7702502
OP here
because of adjacency to parenthesis, then, is the answer. if it were simply 111/3x37 the answer would be 1369
otherwise left to right. neither has precedence, whereas division or multiplication have it over addition/subtraction
and the order doesn't matter with addition & subtraction, but it does with division and multiplication only when division is on the left. When multiplication is on the left the order doesn't matter.
/thread
greetings from /pol/, and good day
>>7705180
then again,
>>7705191
*is if / means
*tho they
I'm high
Division and subtraction, are a subsect of multiplication and addition.
then 1 divided by 3 is the same as 1*1/3
and 1-3 is the same as 1+(-3)
then you should see, that any ambiguity is fucking trivial.
\[n!=\int_0^\infty x^n \div e^x dx\]
>>7702381
Subtraction really is just addition, so it doesn't matter where you do it. Same goes for division.
>>7702502
Ambiguous cause there's no operator between 3 and 37
>>7705279
between the 3 and 37 is clearly multiplication
>>7702381
>what comes first
Your mom.
First addition then subtraction also multiplication then division
I like the notation [math]a/b = a \cdot \frac{1}{b}[/math] and more generally
[math]a_1/a_2/ a_3/\dots/ a_n = a_1\cdot \frac{1}{a_2}\cdot \frac{1}{a_3}\dots\cdot \frac{1}{a_n}[/math]
Just like [math]a-b = a+(-b)[/math]
There are really only two operations (and inverses)
Now lets hope 4chan doesn't shit its pants with this LaTeX
>>7705654
Was about to post something along these lines. Good post anon.
No matter. If we consider addition and subtraction, equiping integers, rationals, reals or complex numbers with addition gives a group, and associativity holds. Subtracting a number is the same as adding a negative version of the same number, so subtracting is just adding the inverse element (which is in the group). From a(bc)=(ab)c, it follows that the order is irrelevant. The same holds for multiplication and division, but with rationals, reals or complex numbers after 0 has been removed.
PEMDAS
>>7702414
would have thought it was something with fluid dynamics, something literaly overflowing
>>7702381
Subtraction is defined as addition of the negative.
Division is defined as multiplication of the inverse.
i always did left 2 right
>>7702381
PEMDAS
in the case where you have M and D, it's left to right.
same with A and S.
gradeschool?
