Pythogora
real
In maths, the term there are two main meanings to the word inverse - both of which are very closely related. Simple answer in the last three paragraphs. A binary operation, defined on a group of numbers is a rule that tells you how to combine two numbers to get a third. Each binary operations (@) has an identity element, generally denoted by i, such that: x@i = x = i@x for all x in the group. Then, for each element x, there is an element in the group, denoted by x-1 (or the inverse of x) such that x@x-1 = i = x-1@x All this may sound rather technical. So here it is in simpler terms: two everyday examples of binary operation are addition and multiplication. The identity for addition is 0. The identity for multiplication is 1. The inverse of x, under addition, is -x. Under multiplication it is 1/x (not defined for x = 0). These give rise to inverse binary operations: subtraction for addition and division for multiplication.
To any set that contains it! It belongs to {sqrt(30)}, or {45, sqrt(30), pi, -3/7}, or irrational numbers, or real numbers between -6 and 6, or all real numbers or complex numbers, etc.
By adding up all the numbers in the group and dividing by the number of numbers in the group.
All the elements in a group must be invertible with respect to the operation. The element 0, which belongs to the set does not have an inverse wrt multiplication.
I believe it is because 0 does not have an inverse element.
No. The inverses do not belong to the group.
Pythogora
They make up the Real numbers.
It belongs in the irrational group of numbers.
real
s
Some would say that there is no intersection. However, if the set of irrational numbers is considered as a group then closure requires rationals to be a proper subset of the irrationals.
array
Pi is an Irrational number, which is one of the two subcategories of real numbers.
Pi is both an irrational number and a transcendental number.