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Thread: Maths language

  1. #1
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    Maths language

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

    1) a function $\displaystyle 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 $\displaystyle f_x : (-c,c) \mapsto R $
    2) $\displaystyle P(X \in R \setminus \{x_1,x_2\})$
    3) Random variable $\displaystyle T_1 = inf\{i \leq 0: \epsilon_{i+1}=1\} $
    4) A probability measure on a sample space $\displaystyle \Omega$ is a function A $\displaystyle \mapsto$ P(A) of event $\displaystyle A \subseteq \Omega$
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  2. #2
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    Re: Maths language

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

    1) a function $\displaystyle 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 $\displaystyle f_x : (-c,c) \mapsto R $
    function $\displaystyle f_x$ 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) $\displaystyle P(X \in R \setminus \{x_1,x_2\})$
    Assuming that "P" here is probability, not "power set", This is the probability that the variable X is any real number other than $\displaystyle x_1$ or $\displaystyle x_2$.

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

    4) A probability measure on a sample space $\displaystyle \Omega$ is a function A $\displaystyle \mapsto$ P(A) of event $\displaystyle A \subseteq \Omega$
    $\displaystyle A\subseteq \Omega$ says that A is a subset of $\displaystyle \Omega$ so this says that a probability measure is a function that assigns a value, P(A), to every subset A of $\displaystyle \Omega$. (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".)
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  3. #3
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    Re: Maths language

    Thank you for your reply.
    I have some further questions about them.
    a) what's the difference between the arrow in (1) and (2)?
    b) Is 'map to' means 'the outcome is'?
    c) I still don't understand (3). Please explain in plain English. Yes $\displaystyle \epsilon$ is binary (0 or 1). Does inf mean the smallest of the set?
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  4. #4
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    Re: Maths language

    Any one can help with this?
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