Q: Defined real numbers

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Because irrational numbers are defined as real numbers which are not rational.

Because irrational numbers are defined as all real numbers which are not rational.

Yes.

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.

The different names for Numbers are defined as Natural numbers, whole numbers , real numbers, decimal numbers, integers, rational numbers and irrational numbers.

Related questions

Because in real numbers they are not defined.

Because irrational numbers are defined as real numbers which are not rational.

Because irrational numbers are defined as all real numbers which are not rational.

Yes irrational numbers are real numbers that are part of the number line,

Yes.

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.

No. The intersection of the two sets is null. Irrational numbers are defined as real numbers that are NOT rational.

There are rational numbers and irrational numbers. Real numbers are DEFINED as the union of the set of all rational numbers and the set of all irrational numbers. Consequently, all rationals, by definition, must be real numbers.

Real numbers are defined as the set of rational numbers together with irrational numbers. So rationals are a subset of reals, by definition.

The different names for Numbers are defined as Natural numbers, whole numbers , real numbers, decimal numbers, integers, rational numbers and irrational numbers.

The imaginary number (i) is defined as the square root of -1. If you multiply i by i you get -1

Yes but only if the denominator is 0 (so the quotient is not defined).