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  1. The notation $\{0,1\}^n$ refers to the space of all $n$-length vectors consisting of $0$s and $1$s, while the notation $[0,1]^n$ ($(0,1)^n$) refers to the space of all $n$-length vectors consisting of real numbers between $0$ and $1$ inclusive (exclusive).

  2. A⇒B means that if A is true, B must also be true, but if A is false, B is unknown. x=3⇒x 2 =9, but x 2 =9⇒x=3 is false, because x could also be -3.

  3. The most basic symbols are the decimal digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9), and the letters of the Latin alphabet. The decimal digits are used for representing numbers through the Hindu–Arabic numeral system.

  4. X ~ N(0, 1) means the cumulative distribution function of X equals the normal (0, 1) cumulative distribution function. So saying X ~ N(0, 1) specifies for any set A the probability that X lies in A; that is, the distribution of X.

  5. The notation $[0,1)$ refers to the set of all real numbers $x$ such that $0\le x\lt 1$. Another common notation for this set is $[0,1[$; which is more common often depends on the language in which the author was educated.

  6. The interval [0, 1) = {x | 0 ≤ x < 1}, for example, is left-closed and right-open. The empty set and the set of all reals are both open and closed intervals, while the set of non-negative reals, is a closed interval that is right-open but not left-open.

  7. 27 maj 2024 · Python operators are special symbols or keywords used to perform specific operations. Depending on the operator, we can perform arithmetic calculations, assign values to variables, compare two or more values, use logical decision-making in our programs, and more. How Operators Work.

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