Forum: ell.stackexchange.com
Tags: <mathematics><reading-aloud>
Title: How do you read these mathematical expressions aloud?
Question: (both above are from  Wikipedia.org )

Answers:
sents: text: Here's how I'd say the first one: The absolute value of S minus the sum from 1 to n of f of t sub
text: i times delta sub
text: i is less than epsilon.
text: Key: (1)
text: The absolute value of (2) S minus (3) the sum from 1 to n of (4) f of t sub
text: i (5) times
text: delta sub
text: i (6) is less than epsilon Note: Some mathematical expressions can be read aloud in more than one way.
text: For example, someone might say: sigma instead of the sum of the function instead of f of delta
text: i instead of delta sub
text: i t sub
text: i delta sub
text: i instead of t sub
text: i times delta sub
text: i
answer_details: author: ell.stackexchange.com/users/113/J.R.
score: 24
sents: text: The absolute value of the difference between S and the sum from i equals one through
text: i equals n of the function f evaluated at t sub
text: i times the width of each i is less than epsilon.
text: If it is clear that i and n are one-indexed, then "the sum from i equals one through
text: i equals n" can be replaced by "the sum of the first n terms".
text: "The width of each i" is an interpretation of "delta i".
text: The function is one divided by the quantity x plus one close quantity, all divided by the square root of x.
text: The integral from zero to infinity of the function d x equals the limit as s goes to zero of the integral from s to 1 of the function d x plus the limit as t goes to infinity of the integral from 1 to t of the function d x.
text: "Goes to" can be replaced by "goes toward", or (as Damkeng suggests) "tends to", or (as J.R. suggests) "approaches".
text: I often use a notation like "integral from x equals a to x equals b" instead of "integral from a to b".
text: I also often say "to positive infinity" instead of "to infinity".
text: I "factored out" the definition of the function in the first sentence.
text: If the function were easy to say (such as "x squared"), I would not "factor out" the definition of the function.
text: Instead, I would include the "x squared" in the statements of the integrals, a la Damkeng's answer.
answer_details: author: ell.stackexchange.com/users/9100/Jasper
score: 15
sents: text: Absolute value of s minus sum
text: i equals one to n, of f of t
text: i times delta
text: i, is less than epsilon.
text: Integral from zero to infinity of dx by x plus one times square root of x is equal to the limit of integral from s to one of dx by x plus one times square root of x as s tends to zero plus the limit of integral from one to t of dx by x plus one times square root of x as t tends to infinity.
text: Please note that this is a casual reading.
text: It's practically impossible to avoid ambiguity when reading mathematical expressions aloud.
text: We might try to add more words such as "left parenthesis", "right parenthesis", and so on, but that wouldn't help much.
text: There are several possible alternatives, but this is how I normally read them.
answer_details: author: ell.stackexchange.com/users/3281/Damkerng T.
score: 9
sents: text: Although not a direct answer to your question, here are a few references on how to read mathematical symbols and expressions.
text: As a non-native English speaker who has to read mathematical formulae, I've found them pretty useful.
text: Handbook for Spoken Mathematics , Research and Development Institute, Inc
text: : This is probably the most complete reference.
text: Not of easy consultation, though.
text: H. Valiaho, Pronunciation of mathematical expressions (pdf):
text: A short list divided by topic (e.g. Logic, Sets, Functions etc.).
text: Reports also variants.
text: K. Kromarek, Mathematics Pronunciation Guide
text: : This is a guide on how to pronounce mathematical symbols and names, but not on how to read expressions.
answer_details: author: ell.stackexchange.com/users/11324/Massimo Ortolano
score: 9
sents: text: The simple answer is "you don't".
text: Complex mathematical expressions like those become ambiguous when read out loud because you lose a lot of the structure.
text: If you ever need to communicate the expression exactly, you'd write it down and point to it.
text: The only exception I can think of is if you were dictating something over the telephone, for example because you were working on a paper with somebody and you were trying to point out a mistake.
text: Then, you'd read out literally every symbol.
text: (Or just the part with the mistake, e.g., "The sum should be from
text: i equals 0 to n minus 1, not 1 to n.")
answer_details: author: ell.stackexchange.com/users/4468/David Richerby
score: 3
sents: text: As a mathematician, a physicist and a uni lecturer, I would read the two expressions above as follows: (1) the absolute value of S minus the sum of "f at t sub
text: i" times "delta sub
text: i", where i changes from 1 to n, is less than epsilon.
text: (2) the x integral from zero to infinity of the function "1 over '(x plus 1) times (square root of x)' " is equal to the limit of x integral from s to 1 of the function as s tends to zero, plus the limit of x integral from 1 to t of the function as t tends to infinity.
text: At a class, you point to the relevant positions of the expressions while you read them.
text: Note that clarity and simplicity in statements are important in teaching.
answer_details: author: ell.stackexchange.com/users/109471/Wilford Lie
score: 1

Summary of the answers:
The simple answer is "you don't". Complex mathematical expressions like those become ambiguous when read out loud because you lose a lot of the structure.
Mathematical expressions become ambiguous when read aloud and this should be avoided.