# Let's suppose vs. Let us suppose

Imagine you are working on a formal research paper (several authors).At the time of making an asumption, what would be more correct:

Let us suppose that.

Imagine you are working on a formal research paper (several authors).At the time of making an asumption, what would be more correct:

Let us suppose that.

I found this in a book:

Suppose we have a collection of blog posts where each document was a post.Shouldn't it be:

Suppose we have a collection of blog posts where each document is a post.

This is a question regarding punctuation, I suppose.This is a question regarding punctuation I suppose.

In informal English we often say "I suppose" to mean "I assume" or "I guess.Am I right in thinking that it should be "I suppose" here?

I faced the sentences:

They are suppose to take a short term view and build product and keep customers satisfied.html)

Does suppose acts here as a noun?

Let $A$ is a $C^*$-algebra and $\mu \in A^{**}$.Suppose that $a \mu = \mu a$ for all $a \in A$.

Suppose that $H$ is a locally finite group and suppose that $H$ let be a FC-group.Let $x \in G$.

Suppose $A=C_{\mathrm{Aut}(G)}(s)$.Suppose $A=C_{\mathrm{Aut}(G)}(s)$.

Suppose that $T$ acts (algebraically) on some vector space $V$ (over the same field $K$).Suppose that $U_1$ is some subgroup of $U$.

Suppose, the white line in the picture (681x262 px) has the slope of 0.And, suppose, (0,0) is at the upper left.

Suppose we have a homomorphism $p:E \rightarrow X.$

Suppose $x \in X$, then we choose $U=E$.

Suppose $A $ and $X$ are random variables and suppose we have $VaR_u(AX)=5$.Furthermore, suppose we are interested in the following probability $P(AX>VaR_u(AX)|A=a)$.

Showing (b) implies (c):

Suppose (b).Showing (c) implies (a):

Suppose (c).