"Assume something be" or "Assume something is"?

Question

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"?

Answer 1

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.

Answer 2

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.