# 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.

or

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

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.

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 $x \in G$.

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 $x\in S$.

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 $Y$.

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.

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?

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

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 $g(x) = \frac{1}{f(x)}$.

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 $a\in X$.

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

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

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

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.

Suppose I have a function $u(x)=x^{0.5}$ if $x>0$ and $u(x)=a(-x)^{0.

Under a ring, suppose for any $x$, $x^n = x$.Then for any $x$, $x + x = 0$ for additive identity $0$.

Suppose $Y\subseteq X$ and $X$ is countable.Since $X$ is countable, $\exists f:\mathbb{N} \to X$ and $f$ is bijection.

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