Yes - except that you need to specify ratios of INTEGERS.
pi/2 is a ratio of pi and 2 but it is irrational.
There are numbers which cannot be expressed as ratios of two integers. These are called irrational numbers.
Irrational numbers can't be expressed as fractions .
These are the numbers which cannot be expressed as ratios of two integers.
No.
Because irrational numbers are defined as all real numbers which are not rational.
Because irrational numbers are defined as real numbers which are not rational.
No. The intersection of the two sets is null. Irrational numbers are defined as real numbers that are NOT rational.
Because they cannot be expressed as ratios of integers.
Because there are numerical values which cannot be expressed as ratios of two integers. That is, there are numbers that are not rational.
irrational numbers are those which are inexpressible as ratios of two whole numbers. any whole number w can be expressed as w/1.
The set of real numbers is defined as the union of all rational and irrational numbers. Thus, the irrational numbers are a subset of the real numbers. Therefore, BY DEFINITION, every irrational number is a real number.
In mathematics it means numbers which cannot be represented by ratios of two integers.