Suppose/assume that or supposing/assuming that

or

Supposing/assuming that X equals 1, we know X+1=2.In maths the forms suppose or assume are widely used.

Pade approximation of a rational function

So suppose I have two rational functions $R_1(x)$ and $R_2(x)$, i.Next, suppose that $R_1(x)$ is fixed and I want to approximate $R_1(x)$ with $R_2(x)$ where the polynomials in $R_2(x)$ have strictly lower degree, i.

A polynomial recovery problem

Suppose we know $deg(m(x))=n-1=deg(f_1(x))=deg(f_2(x))$.Suppose we know $C_1(x),C_2(x)$ where $deg(C_i)=n$.

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

name for a subset of a binary relational structure which is “closed downward”?

Let $X$ be a set and suppose that $R$ is a binary relation on $X$.Suppose further that $S\subseteq X$ has the property that whenever $y\in S$ and $xRy$ ($x\in X$), then also $x\in S$.

semi-continuity of sheaves

Suppose $i: Y\subset X$ is a closed subvariety of a variety $X$.Suppose there is an exact sequence of coherent sheaves on $X$:
$$0\rightarrow A \rightarrow B\rightarrow i_*C\rightarrow 0$$

Suppose $C$ is locally free on $Y$.

Integrating over the real points of an algebraic variety

Suppose I have some algebraic variety $X/\mathbb R$ of dimension $n$, and suppose that $X(\mathbb R)$ is compact.Now for any element of $H^0(X,\Omega_X^n)$ (i.

X not simply connected and X-x contractible

Suppose $X$ is a CW-complex which is not simply connected and there is a point $x\in X$ such that $X-x$ is contractible.Is $X$ homotopy equivalent to a wedge of circles?

Advanced Calculus - Functions, Sequences, and Limits (Fulks) [on hold]

Suppose that f(x)→A, h(x)→A as x→∞, and f(x)≤g(x)≤h(x).Show that g(x)→A as x→∞.

How far is ﻿Lindelöf from compactness?

Then, $X$ is compact if and only if $X^{\kappa}$ is ﻿Lindelöf for any cardinal $\kappa$.So suppose that we have a space $X$ that is not compact, but
$X^{\omega_1}$ is Lindelöf.

Suppose $f$ is a measurable function and $f(x) > 0$ for all $x$. Let $g(x) = \frac{1}{f(x)}$. Prove that g is a measurable function.

Suppose $f$ is a measurable function and $f(x) > 0$ for all $x$.Let $g(x) = \frac{1}{f(x)}$.

Prove that $f_a(x)$ belongs to $C(X)$ for any $a\in X$

Suppose that $(X,d)$ is a metric space, and $a\in X$.Consider the function
$$f_a(x)=d(a,x)$$
Prove that $f_a(x)∈C(X)$ for any $a\in X$.

why is a homomorphism a cover space?

Suppose we have a homomorphism $p:E \rightarrow X.$
Suppose $x \in X$, then we choose $U=E$.

Question on Continuous Differentiability under Expectation

Suppose $f(x)$ is continuously differentiable in $x \in \Re$ a.e.

Suppose that $F(x):=\int_{-\infty}^x f(t)dt$ is finite for all $x$. Prove that $F$ is continuous.

Let $f$ be a nonnegative, measurable function on $\mathbb{R}$, and suppose that $F(x):=\int_{-\infty}^x f(t)dt$ is finite for all $x$.Suppose that $F(x)$ is finite for all $x$, then $F(x)$ is uniformly bounded.

Bound on the kth moment of the mean of X

Suppose we have $X_1, X_2,.We put$X=X_1+.