Does PEMDAS Apply to All Math Equations?

[SigmaS]

I was told PEMDAS isn't always followed, particularly in higher level math.
Is this true? Because I recall the purpose of PEMDAS is to prevent ambiguity, and without it, at any level, would result in ambiguity, even though it's just a convention and not something we can really prove.

Also, when you reword equations are you still relying on the concept of PEMDAS? Like, for example, to say $\frac{5}{3}n=15 \equiv 5n=45$ is to validate PEMDAS, yes?

 

[I like Serena]

I was told PEMDAS isn't always followed, particularly in higher level math.
Is this true? Because I recall the purpose of PEMDAS is to prevent ambiguity, and without it, at any level, would result in ambiguity, even though it's just a convention and not something we can really prove.

Also, when you reword equations are you still relying on the concept of PEMDAS? Like, for example, to say $\frac{5}{3}n=15 \equiv 5n=45$ is to validate PEMDAS, yes?

Hi SigmaS, welcome to MHB! ;)

In higher level math we don't always deal with regular multiplication and addition.
Even then, PEMDAS is usually applied, since it does indeed eliminate ambiguity without being wordy about it.
And yes, this is international convention, so we can always assume it.

In $\frac{5}{3}n=15$ there is no ambiguity. The division is specified in such a way that it has to come first - as if it was in parentheses. So PEMDAS is irrelevant here. It only becomes relevant when we type it into a calculator, because then PEMDAS requires us to use parentheses. That is, we have to type [M]( 5 / 3 ) * n[/M] to get what was written.

Anyway, there is no need to 'validate' PEMDAS. It's just a rule that says when parentheses can be omitted without changing the expression.
The parentheses cannot be omitted in for instance $5/(3\times n)$, because $5/3\times n$ means something different.
It's different with $(5/3)\times n$, since that is the same as $5 / 3 \times n$.
In case of doubt, we should add parentheses first — according to PEMDAS — and then reword the equation.