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I am writing a scientific paper.

I am not sure about the usage of "assume."

Should I say "Let us assume x is real," or should I say "Let us assume x be real"?

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    Your final alternative suggests you may be confusing the construction Let's assume [statement] [is a true statement] with the textbook standard Let [variable] be [value]. – FumbleFingers Mar 22 '17 at 13:56
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    Just so it's said, "sth" is not a word. I wish its use would die. – cHao Mar 22 '17 at 18:18
  • What is "sth"...it shows up a ton in the Related sidebar – Nick T Mar 22 '17 at 20:48
  • @NickT It's an abbreviation for "something". – Catija Mar 22 '17 at 21:28
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Let us assume x is real

This sounds about right.

Let us assume x be real

This is grammatically incorrect.

Let us assume x to be real

This is grammatically correct, but sounds awkward, though with more context, it could be more correct than is.

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    In some contexts, "Let x be [any] real" works also. (And FWIW, in a paper/proof, the "to be" construction above would sound perfectly fine to me.) – A C Mar 22 '17 at 17:31
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Your question has made me think about this for the first time: there seems to be a distinction between verbs that merely process information about a fixed situation, and verbs that declare a position or approach to a potentially changeable situation.

For example you would say

I believe [that] X is real.

and not "I believe X be real". By contrast you should really say

I demand [that] X be real.

and not "I demand X is real".

One result of this is that the following two statements have different meaning:

I insist that X is real

means "I emphatically believe that the proposition 'X is real' describes the current situation correctly, independent of my intervention or yours", whereas

I insist that X be real

means something along the lines of "I am laying down the law, that you must ensure X is real", or more generally "X may be real or not, but if it is not real then I will refuse to proceed/cooperate with whatever we're talking about".

Your example, of assuming whether something is real, is processing information about a fixed proposition. Therefore you would not use the subjunctive. You would say "assume that X is real", not "assume that X be real".

In a mathematical paper where are you are describing your initial conditions, you can choose whether to use the metaphor of actively creating X as you define it ("let X be a real number") or the metaphor of merely describing the state of an already-defined entity ("assume X is a real number"). The former is probably more common.

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