0

I've struggled to find in google the exact definition of the word "orders" as used in bodmas's second operation. I know what it means (powers, indeces etc.) but I'm looking for the proper mathematical definition and how I could use it in a sentence. Can I say for example "3 raised to the order 2"?

Edit to add: I'm referring to the "orders" in the mnemonic as in brackets, orders, division etc. where orders means powers. Not about order in "order of operations".

Eva
  • 1
  • 3
  • Order of operations means the sequence : first, second,... to be followed performing the arithmetical operations. – Mauro ALLEGRANZA Sep 11 '19 at 15:02
  • The word "order" is used in a variety of ways in mathematics. Your "BODMAS" is a made-up word, a mnemonic to help one remember the usual *precedence" of operations in arithmetic expressions. – hardmath Sep 11 '19 at 15:02
  • 1
    I'm asking about the use of orders as in brackets, orders, division, multiplication etc. not as in order of operations. – Eva Sep 11 '19 at 15:03
  • The word order is mainly used in mathematics for a structure whose definition is well known. It is very useful that synonyms are not used in mathematics but nevertheless it is actually used in particular for "order of growth of a function", "differential equations of such order" "square matrices of order n" and some others I suppose. But I have never heard "" 3 raised to the order 2 "and would ensure that such an expression should be avoided. – Piquito Sep 11 '19 at 15:06
  • Another common acronym for this is PEMDAS, where in place of "orders" we have the exponents operation. – hardmath Sep 11 '19 at 15:07
  • Old use; see Order (degree). – Mauro ALLEGRANZA Sep 11 '19 at 15:24
  • Mauro, that is great. Thanks! – Eva Sep 11 '19 at 15:30

2 Answers2

1

"BODMAS" may well be taught before students have even encountered the notion of exponentiation. In that context it really should be "BDMAS"*, but of course this is not readily pronounceable so an "O" was added. The explanation I was given at school was that this stood for "of" (i.e. the other things can be inside the brackets), which doesn't really mean anything. I suspect "order" was just a post-hoc attempt to make this include exponentiation without changing the acronym; it's not used with that meaning elsewhere in mathematics.

*or really "$\mathrm{B}^\mbox{D}_\mbox{M}{}^\mbox{A}_\mbox{S}$" since D/M (mostly) have equal precedence, as do A/S, but that's even harder to say.

Especially Lime
  • 40,828
0

There is no mathematical definition of orders. It's used here as a collective lay term and not as a proper mathematical one.

Vasily Mitch
  • 10,129