Editing Openai/68a11068-3fe8-8007-bd18-674462ff2b41 (section)

=== Assistant: You’ve put your finger on something important 👌. ===
You’ve put your finger on something important 👌.

You’re absolutely right: in professional mathematics, nobody is thinking in terms of “PEMDAS.” That’s a pedagogical crutch used in grade school to help beginners remember operator precedence.

===== 1. Stacked fractions, exponents, parentheses are always used to avoid ambiguity. - A mathematician wouldn’t write ac/bcac/bcac/bc. They’d write either acbc\frac{ac}{bc}bcac or (ac/b)c(ac/b)c(ac/b)c. =====
# Implicit multiplication is the norm, but it’s always written so context makes it clear. - e.g. πr2\pi r^2πr2, 2x2x2x, ababab.
# Linear slash notation (like /) is discouraged except in quick notes or programming, because it is ambiguous in algebraic text.

===== - It’s a didactic shortcut for students who can’t yet parse algebra structurally. =====
'' In computing, the left-to-right convention for / and '' comes from programming language design (C, Python, etc.), not from mathematics itself.

===== Instead of “PEMDAS,” what you see is: =====
* Explicit grouping: ……\frac{…}{…}……, parentheses, brackets.
* Structural reasoning: manipulating expressions symbolically, not “running an order-of-ops checklist.”
* Avoidance of ambiguity: clarity > conciseness.

That’s why professional papers never write things like 50/2(1+4)50/2(1+4)50/2(1+4). It’s bad notation, not “deep math.”

✅ So: you’re absolutely correct — PEMDAS is a training wheel. In real math, the standard is explicit grouping to avoid ambiguity, not reliance on a mnemonic.

Would you like me to show you how the same expression looks in three different worlds —
# grade-school PEMDAS style,
# programming/calculator style,
# professional mathematics style — so you can see exactly why this confusion happens?