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A mathematical approach:

Yes they are. Irrational Numbers are very real, for example - the square root of two - which is irrational (but can be plotted in a number line without difficulty with a compass and straight edge). All numbers you can think of (even if you cant white them out) are real numbers.

They are real, but they can't be expressed as fractions.

A philosophical approach:

According to ME, there should be a limit. If there is a number which is not ending, we can't say that it is a number because it has not ended yet, its not a complete number. That's why, any number which is not ending is not a number, so irrational numbers and some rational numbers are not numbers and we can't plot them on real line, no matter how much depth we are into it. If there is a number 1.0000... (100 million 0's) ...1, we can plot it by dividing real line into required many parts but we cant plot a number like 1.1111....1111....(up to, we don't know), actually that's not a number yet.

Maths should be changed.

Q: Are irrational numbers real numbers

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Irrational numbers are real numbers.

No. All irrational numbers are real, not all real numbers are irrational.

No. Irrational numbers by definition fall into the category of Real Numbers.

All irrational numbers are real, but not all real numbers are irrational.

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.

Related questions

No, but the majority of real numbers are irrational. The set of real numbers is made up from the disjoint subsets of rational numbers and irrational numbers.

False. Irrational numbers are real numbers.

Irrational numbers are real numbers.

No. All irrational numbers are real, not all real numbers are irrational.

Irrational numbers are real numbers.

No. Irrational numbers by definition fall into the category of Real Numbers.

All irrational numbers are real, but not all real numbers are irrational.

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.

Irrational numbers are real numbers because they are part of the number line.

No. Irrational numbers are real numbers, therefore it is not imaginary.

An irrational number is any real number that cannot be expressed as a ratio of two integers.So yes, an irrational number IS a real number.There is also a set of numbers called transcendental numbers, which includes both real and complex/imaginary numbers. Of this set, all the real numbers are irrational numbers.

Both irrational and rational are real. Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.