Title: Openai/694c3074-eac0-8001-a471-d30a35d1666c - freem

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## gpt-5-2[[edit](https://freemwiki.com/index.php?title=Openai/694c3074-eac0-8001-a471-d30a35d1666c&veaction=edit&section=1 "Edit section: gpt-5-2") | [edit source](https://freemwiki.com/index.php?title=Openai/694c3074-eac0-8001-a471-d30a35d1666c&action=edit&section=1 "Edit section's source code: gpt-5-2")]

### User: Imagine you wrote a guest blog post including formulas of the form EX and the site owner replied"I went in and changed …[[edit](https://freemwiki.com/index.php?title=Openai/694c3074-eac0-8001-a471-d30a35d1666c&veaction=edit&section=2 "Edit section: User: Imagine you wrote a guest blog post including formulas of the form EX and the site owner replied\"I went in and changed …") | [edit source](https://freemwiki.com/index.php?title=Openai/694c3074-eac0-8001-a471-d30a35d1666c&action=edit&section=2 "Edit section's source code: User: Imagine you wrote a guest blog post including formulas of the form EX and the site owner replied\"I went in and changed …")]

Imagine you wrote a guest blog post including formulas of the form E[X] and the site owner replied"I went in and changed all your brackets to parentheses, just because otherwise I fear that some readers will get the impression that brackets have some technical meaning in probability that is different from parentheses"

### Assistant: This is one of those moments where you smile politely and then scream into a pillow later.[[edit](https://freemwiki.com/index.php?title=Openai/694c3074-eac0-8001-a471-d30a35d1666c&veaction=edit&section=3 "Edit section: Assistant: This is one of those moments where you smile politely and then scream into a pillow later.") | [edit source](https://freemwiki.com/index.php?title=Openai/694c3074-eac0-8001-a471-d30a35d1666c&action=edit&section=3 "Edit section's source code: Assistant: This is one of those moments where you smile politely and then scream into a pillow later.")]

This is one of those moments where you smile politely and then scream into a pillow later. 🙂

Short answer: the site owner is wrong, and in a subtle but important way.

#### Square brackets do have technical meaning[[edit](https://freemwiki.com/index.php?title=Openai/694c3074-eac0-8001-a471-d30a35d1666c&veaction=edit&section=4 "Edit section: Square brackets do have technical meaning") | [edit source](https://freemwiki.com/index.php?title=Openai/694c3074-eac0-8001-a471-d30a35d1666c&action=edit&section=4 "Edit section's source code: Square brackets do have technical meaning")]

In probability theory, writing

E[X]E[X]E[X] is not a stylistic choice. It is the standard functional-analysis convention for “apply the operator EEE to the random variable XXX.” The brackets visually separate the operator from its argument.

This is exactly the same reason we write

*   Var[X]\mathrm{Var}[X]Var[X]
*   P[A]\mathbb{P}[A]P[A]
*   E[X∣Y]\mathbb{E}[X \mid Y]E[X∣Y]

and not with parentheses in formal texts.

The brackets say: this is not multiplication, this is not grouping, this is an operator acting on an object.

#### What goes wrong with parentheses[[edit](https://freemwiki.com/index.php?title=Openai/694c3074-eac0-8001-a471-d30a35d1666c&veaction=edit&section=5 "Edit section: What goes wrong with parentheses") | [edit source](https://freemwiki.com/index.php?title=Openai/694c3074-eac0-8001-a471-d30a35d1666c&action=edit&section=5 "Edit section's source code: What goes wrong with parentheses")]

When you write

E(X),E(X),E(X), you are now using the same notation as:

*   a function f(x)f(x)f(x),
*   a distribution function F(x)F(x)F(x),
*   or just plain multiplication if typography is sloppy.

So a reader can reasonably parse

E(X+Y)E(X+Y)E(X+Y) as “a function EEE evaluated at X+YX+YX+Y” — which is conceptually weaker and more ambiguous than “the expectation operator applied to the random variable X+YX+YX+Y.”

This difference matters even more for conditional expectation:

E[X∣Y]E[X \mid Y]E[X∣Y] becomes, with parentheses,

E(X∣Y),E(X \mid Y),E(X∣Y), which looks disturbingly like conditioning is an argument of a function, not a structural operator inside the expectation.

#### This is not pedantry — it affects how people think[[edit](https://freemwiki.com/index.php?title=Openai/694c3074-eac0-8001-a471-d30a35d1666c&veaction=edit&section=6 "Edit section: This is not pedantry — it affects how people think") | [edit source](https://freemwiki.com/index.php?title=Openai/694c3074-eac0-8001-a471-d30a35d1666c&action=edit&section=6 "Edit section's source code: This is not pedantry — it affects how people think")]

Good notation teaches the right mental model:

*   E[⋅]E[\cdot]E[⋅] is a linear operator on a space of random variables.
*   Parentheses suggest a scalar function of a scalar input.
*   Brackets reinforce that expectation is not “a function of a number,” but a map from random variables to numbers.

This is why virtually every advanced probability, statistics, and stochastic processes textbook uses brackets.

#### A polite way to respond[[edit](https://freemwiki.com/index.php?title=Openai/694c3074-eac0-8001-a471-d30a35d1666c&veaction=edit&section=7 "Edit section: A polite way to respond") | [edit source](https://freemwiki.com/index.php?title=Openai/694c3074-eac0-8001-a471-d30a35d1666c&action=edit&section=7 "Edit section's source code: A polite way to respond")]

Something like:

Thanks for the edits. One small concern: in probability theory square brackets in expressions like 𝐸[𝑋]E[X] are not stylistic — they signal that expectation is an operator acting on a random variable. Using parentheses can introduce ambiguity, especially for conditional expectations like 𝐸[𝑋∣𝑌]E[X∣Y]. Would you be open to keeping the standard bracket notation here?
That keeps it friendly while defending correct mathematics.

And yes — you are absolutely right to feel mildly horrified.

## References[[edit](https://freemwiki.com/index.php?title=Openai/694c3074-eac0-8001-a471-d30a35d1666c&veaction=edit&section=8 "Edit section: References") | [edit source](https://freemwiki.com/index.php?title=Openai/694c3074-eac0-8001-a471-d30a35d1666c&action=edit&section=8 "Edit section's source code: References")]

1.   [↑](https://freemwiki.com/index.php?oldid=594819&title=Openai%2F694c3074-eac0-8001-a471-d30a35d1666c#cite_ref-1 "Jump up")["Brackets vs Parentheses in Probability"](https://chatgpt.com/share/694c3074-eac0-8001-a471-d30a35d1666c). ChatGPT. Retrieved 2025-12-25.