1. ## Maths language

I have problem with some mathematics language. Can some one interpret for me?

1) a function $f_x : R \rightarrow [0,\infty]$. Is this means ' function fx consists of variable which is real numbers and the outcome of function fx is from 0 to infinity'?
2) a function $f_x : (-c,c) \mapsto R$
2) $P(X \in R \setminus \{x_1,x_2\})$
3) Random variable $T_1 = inf\{i \leq 0: \epsilon_{i+1}=1\}$
4) A probability measure on a sample space $\Omega$ is a function A $\mapsto$ P(A) of event $A \subseteq \Omega$

2. ## Re: Maths language

Originally Posted by avisccs
I have problem with some mathematics language. Can some one interpret for me?

1) a function $f_x : R \rightarrow [0,\infty]$. Is this means ' function fx consists of variable which is real numbers and the outcome of function fx is from 0 to infinity'?
Yes, though I would use the phrase "consists of". [latex]f_x maps the set f all real number to the set of non-negative real numbers.

2) a function $f_x : (-c,c) \mapsto R$
function $f_x$ maps the open interval (-c, c) (all real numbers strictly larger than -c and strictly larger than c) to the set of all real numbers.

2) $P(X \in R \setminus \{x_1,x_2\})$
Assuming that "P" here is probability, not "power set", This is the probability that the variable X is any real number other than $x_1$ or $x_2$.

3) Random variable $T_1 = inf\{i \leq 0: \epsilon_{i+1}=1\}$
This requires that " $\epsilon_n$" be a set of numbers, some of which may be equal to 1. $T_1$ is the smallest is, less than or equal to 0, such that the $\epsilon$ with subscript i+ 1 is equal to 1.

4) A probability measure on a sample space $\Omega$ is a function A $\mapsto$ P(A) of event $A \subseteq \Omega$
$A\subseteq \Omega$ says that A is a subset of $\Omega$ so this says that a probability measure is a function that assigns a value, P(A), to every subset A of $\Omega$. (Normally a probability is a number between 0 and 1 but that is not stated in your (4) so I just used the word "value".)

3. ## Re: Maths language

c) I still don't understand (3). Please explain in plain English. Yes $\epsilon$ is binary (0 or 1). Does inf mean the smallest of the set?