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Suppose I am giving a math talk and I am going to write on the board Let A be a variable. What do I say while I write? Can I say Let's let A be a variable or should I write We let A be a variable and say the same thing?

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I think there's a certain amount of "crosstalk" between computer programming languages and spoken English here. Yes, it's perfectly possible to say/write any of OP's alternatives, but they're all a bit "geek speak". I'd either say Create [or Assume] a variable A, or more likely Call the first variable A (since there are probably going to be others). –  FumbleFingers Nov 3 '11 at 21:40
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"Let's let.." sounds fine to me - I hear math lecturers use it all the time. –  BlueRaja - Danny Pflughoeft Nov 4 '11 at 6:32

5 Answers 5

up vote 16 down vote accepted

You should simply write and say

Let A be a variable

and the audience will understand what you are conveying.

Let us let A be a variable

and

We let A be a variable

are fine but unnecessarily long.

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In all the cases the audience will understand. I was wondering which one is both correct and helps to engross the audience most. –  Alessandro Nov 3 '11 at 19:49

I'd use "Let A be a variable" in speaking, too.

"Let's let A..." is correct grammatically, but sounds unnatural.

I wouldn't use "Let us A...", it isn't correct.

"We let A be..." is correct, but I insist that the first option is the best one.

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Let's let A ... is grammatical. Let us A be... is not.

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sorry, I meant "We let A be...", not "let us A be". I edited the post accordingly. –  Alessandro Nov 3 '11 at 19:44
    
Then 'We let A be...' is also grammatical. –  Barrie England Nov 3 '11 at 19:51

I would say Let x be variable and I would avoid using A. The reason is that a is already an overloaded letter in English and it's not immediately clear whether you are about to introduce a singular noun (e.g., Let a cat out of the house.) or the name of a variable.

Another useful phrase would be Let lambda equal as it's likely you are about to introduce the definition of a variable. If you are talking about a variable that's in the middle of an equation, you could just use a declarative: mu is variable or c is constant.

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You're a teacher. Communication is possibly more important than correctness. For this reason, I would use:

Let A be a variable.

Also, this is posed as a command to your students, which is applicable in your situation.

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Why quotes? In speaking, you would not say the quotes, and in printed mathematical work you would use italics: Let A be a variable. –  GEdgar Nov 4 '11 at 13:10
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@GEdgar, because I'm sick and not thinking straight. Thanks for pointing that out. –  Hand-E-Food Nov 6 '11 at 21:49

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