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In p.251, "Introduction to statistics and probability for engineers and scientists, Sheldon M.Ross, 6th edition", I found this sentence:

By equating to zero, we obtain that the maximum likelihood estimate lambda_hat equals (some value).

For which the author means: To equate some equation (in previous page of the book) that contains lambda_hat (the so-called maximum likelihood estimate) to zero to solve for lambda_hat.

It's not clear to me that this is a case of bad grammar, a typo or a usage of the implicit object or something I'm being unaware of?

Also I couldn't find in any popular online dictionary such phrase "By equating to (something)".

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  • equate to something: to be the same in amount, number, or size: The price of such goods in those days equates to about $50 at current prices. dictionary.cambridge.org/dictionary/english/equate-to
    – user 66974
    Commented Oct 3, 2023 at 5:21
  • The first three "popular dictionaries online" that come up on Google do mention it...
    – fev
    Commented Oct 3, 2023 at 6:41
  • 2
    Note that you can equate an expression or a variable to zero, not an equation. This sort of wording is more common in Maths lectures than books or papers, which are more formal .
    – Peter
    Commented Oct 3, 2023 at 6:42
  • @user66974 That's "Something equates to something else", here is "By equating to something else". One may ask equating (what?) to something else.
    – Tran Khanh
    Commented Oct 3, 2023 at 7:23
  • 1
    "By setting to zero" seems more usual, in my experience.
    – Stuart F
    Commented Oct 3, 2023 at 8:33

1 Answer 1

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It will be

  • finding where the derivative is zero
  • by taking an expression for the derivative,
  • equating the expression to zero (which means forming an equation by sticking "=0" on the end; ELU has a bad zero)
  • and solving the resulting equation.
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  • Yes, normal math talk after referring to the expression: "By equating to 0, ..."
    – Yosef Baskin
    Commented Oct 3, 2023 at 15:59

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