Firstly, don’t forget exponents come before multiply/divide. More importantly, neither defines wether implied multiplication is a multiply/divide operation or a bracketed operation.
The only confusion I can see is if you intended for the 4 to be an exponent of the 3 and didn’t know how to do that inline, or if you did actually intend for the 4 to be a separate numeral in the same term? And I’m confused because you haven’t used inline notation in a place that doesn’t support exponents of exponents without using inline notation (or a screenshot of it).
As written, which inline would be written as (2^3)4, then it’s 32. If you intended for the 4 to be an exponent, which would be written inline as 2^3^4, then it’s 2^81 (which is equal to whatever that is equal to - my calculator batteries are nearly dead).
we don’t have a standard
We do have a standard, and I told you what it was. The only confusion here is whether you didn’t know how to write that inline or not.
It’s ambiguous because it works both ways, not because we don’t have a standard.
Try reading the whole sentence. There is a standard, I’m not claiming there isn’t. Confusion exists because operating against the standard doesn’t immediately break everything like ignoring brackets would.
Just to make sure we’re on the same page (because different clients render text differently, more ambiguous standards…), what does this text say?
234
It should say 2^3^4; “Two to the power of three to the power of four”. The proper answer is 2⁸¹, but many math interpreters (including Excel, MATLAB, and many students) will instead compute 8⁴, which is quite different.
We have a standard because it’s ambiguous. If there was only one way to do it, we’d just do that, no standard needed. You’d need to go pretty deep into kettle math or group theory to find atypical addition for example.
Ah ok. Sorry, got caught out by a double negative in your sentence.
Confusion exists because operating against the standard doesn’t immediately break everything like ignoring brackets would
Ah but that’s exactly the original issue in this thread - the e-calc is ignoring the rules pertaining to brackets. i.e. The Distributive Law.
Ah ok. Well that was my only confusion was what you had actually intended to write, not how to interpret it (depending on what you had intended). Yes should be interpreted 2^81.
including Excel
Yeah, but Excel won’t let you put in a factorised term either. It’s just severely broken because the people who wrote it didn’t bother checking the rules of Maths first. Programmers not knowing the rules of Maths doesn’t mean Maths is ambiguous (it certainly creates a lot of confusion though!).
We have a standard because it’s ambiguous. If there was only one way to do it, we’d just do that,
Disagree. There is one way to do it - follow the rules of Maths. That’s why they exist. The order of operations rules are at least 400 years old, and make it not ambiguous. If people aren’t obeying the rules then they’re just wrong - that doesn’t make it ambiguous. It’s like saying if e-calcs started saying 1+1=3 then that must mean 1+1 is ambiguous. It might create confusion, but it doesn’t mean the Maths is ambiguous.
It’s BE(D=M)(A=S). Different places have slightly different acronyms - B for bracket vs P for parenthesis, for example.
But, since your rule has the D&M as well as the A&S in brackets does that mean your rule means you have to do D&M as well as the A&S in the formula before you do the exponents that are not in brackets?
But seriously. Only grade school arithmetic textbooks have formulas written in this ambiguous manner. Real mathematicians write their formulas clearly so that there isn’t any ambiguity.
Grade school is a US synonym for primary or elementary school; it doesn’t seem to be used as a term in England or Australia. Apparently, they’re often K-6 or K-8; my elementary school was K-4; some places have a middle school or junior high between grade school and high school.
I was taught that division is just inverse multiplication, and to be treated as such when it came to the order of operations (i.e. they are treated as the same type of operation). Ditto with addition and subtraction.
BDMAS bracket - divide - multiply - add - subtract
BEDMAS: Bracket - Exponent - Divide - Multiply - Add - Subtract
PEMDAS: Parenthesis - Exponent - Multiply - Divide - Add - Subtract
Firstly, don’t forget exponents come before multiply/divide. More importantly, neither defines wether implied multiplication is a multiply/divide operation or a bracketed operation.
The Distributive Law says it’s a bracketed operation. To be precise “expand and simplify”. i.e. a(b+c)=(ab+ac).
Exponents should be the first thing right? Or are we talking the brackets in exponents…
Exponents are second, parentheses/brackets are always first. What order you do your exponents in is another ambiguity though.
No it isn’t - top down.
234 is ambiguous. 2(34) is standard practice, but some calculators aren’t that smart and will do (23)4.
It’s ambiguous because it works both ways, not because we don’t have a standard. Confusion is possible.
The only confusion I can see is if you intended for the 4 to be an exponent of the 3 and didn’t know how to do that inline, or if you did actually intend for the 4 to be a separate numeral in the same term? And I’m confused because you haven’t used inline notation in a place that doesn’t support exponents of exponents without using inline notation (or a screenshot of it).
As written, which inline would be written as (2^3)4, then it’s 32. If you intended for the 4 to be an exponent, which would be written inline as 2^3^4, then it’s 2^81 (which is equal to whatever that is equal to - my calculator batteries are nearly dead).
We do have a standard, and I told you what it was. The only confusion here is whether you didn’t know how to write that inline or not.
Try reading the whole sentence. There is a standard, I’m not claiming there isn’t. Confusion exists because operating against the standard doesn’t immediately break everything like ignoring brackets would.
Just to make sure we’re on the same page (because different clients render text differently, more ambiguous standards…), what does this text say?
It should say
2^3^4; “Two to the power of three to the power of four”. The proper answer is 2⁸¹, but many math interpreters (including Excel, MATLAB, and many students) will instead compute 8⁴, which is quite different.We have a standard because it’s ambiguous. If there was only one way to do it, we’d just do that, no standard needed. You’d need to go pretty deep into kettle math or group theory to find atypical addition for example.
Ah ok. Sorry, got caught out by a double negative in your sentence.
Ah but that’s exactly the original issue in this thread - the e-calc is ignoring the rules pertaining to brackets. i.e. The Distributive Law.
Ah ok. Well that was my only confusion was what you had actually intended to write, not how to interpret it (depending on what you had intended). Yes should be interpreted 2^81.
Yeah, but Excel won’t let you put in a factorised term either. It’s just severely broken because the people who wrote it didn’t bother checking the rules of Maths first. Programmers not knowing the rules of Maths doesn’t mean Maths is ambiguous (it certainly creates a lot of confusion though!).
Disagree. There is one way to do it - follow the rules of Maths. That’s why they exist. The order of operations rules are at least 400 years old, and make it not ambiguous. If people aren’t obeying the rules then they’re just wrong - that doesn’t make it ambiguous. It’s like saying if e-calcs started saying 1+1=3 then that must mean 1+1 is ambiguous. It might create confusion, but it doesn’t mean the Maths is ambiguous.
Brackets are ALWAYS first.
afair, multiplication was always before division, also as addition was before subtraction
It’s BE(D=M)(A=S). Different places have slightly different acronyms - B for bracket vs P for parenthesis, for example.
But multiplication and division are whichever comes first right to left in the expression, and likewise with subtraction.
Although implicit multiplication is often treated as binding tighter than explicit. 1/2x is usually interpreted as 1/(2x), not (1/2)x.
But, since your rule has the D&M as well as the A&S in brackets does that mean your rule means you have to do D&M as well as the A&S in the formula before you do the exponents that are not in brackets?
But seriously. Only grade school arithmetic textbooks have formulas written in this ambiguous manner. Real mathematicians write their formulas clearly so that there isn’t any ambiguity.
That’s not really true.
You’ll regularly see textbooks where 3x/2y is written to mean 3x/(2y) rather than (3x/2)*y because they don’t want to format
3x ---- 2yproperly because that’s a terrible waste of space in many contexts.
That’s what I said.
You generally don’t see algebra in grade school textbooks, though.
12 is a grade. I took algebra in the 7th grade.
Grade school is a US synonym for primary or elementary school; it doesn’t seem to be used as a term in England or Australia. Apparently, they’re often K-6 or K-8; my elementary school was K-4; some places have a middle school or junior high between grade school and high school.
a fair point, but aren’t division and subtraction are non-communicative, hence both operands need to be evaluated first?
It’s commutative, not communicative, btw
whoops, my bad
1 - 3 + 1 is interpreted as (1 - 3) + 1 = -1
Yes, they’re non commutative, and you need to evaluate anything in parens first, but that’s basically a red herring here.
ok, i guess you’re right
Multiplication VS division doesn’t matter just like order of addition and subtraction doesn’t matter… You can do either and get same results.Edit : the order matters as proven below, hence is important
If you do only multiplication first, then 2×3÷3×2 = 6÷6 = 1.
If you do mixed division and multiplication left to right, then 2×3÷3×2 = 6÷3×2 = 2×2 = 4.
Edit: changed whitespace for clarity
2nd one is correct, divisions first.
4 would be correct since you go left to right.
I was taught that division is just inverse multiplication, and to be treated as such when it came to the order of operations (i.e. they are treated as the same type of operation). Ditto with addition and subtraction.
I will never forget this.
BDSM Brackets … ok
Glad to be of help, I remember it being taughy back in the 4th grade and it stuck well.