What does the expression #x in RR# mean ?

3 Answers
Mar 12, 2017

A real number is any rational or irrational number.

For example: #pi, e,2, 4, -78, 1/2, 23/6# and so on

It means that #x# is an element of the set of real numbers which we symbolize with #R#.

Mar 12, 2017

Answer:

It usually means:

"#x# is a member of the set of real numbers"

or more simply:

"#x# is a real number"

Explanation:

  • #RR# usually denotes the set of Real numbers.

  • #in# denotes membership.

So #x in RR#, means that #x# is a member of the set of Real numbers. In other words, #x# is a Real number.

Related expressions are:

  • #AA x in RR" "# meaning "for all #x# in the set of real numbers". in other words: "for all real numbers #x#".

  • #EE x in RR : ..." "# meaning "there exists a member #x# in the set of real numbers such that ..." or "there exists a real number #x# such that ...".

In some kinds of constructive mathematics, where speaking of "the set of Real numbers" is considered a little presumptuous, the expression "#x in RR#" may be read as "#x# is a real number" and #AA x in RR# understood as "for any real number #x#", etc., avoiding the concept of a completed set of real numbers.