All real numbers are irrational

Answer 1

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.

Answer 2

No.

By definition, a real number has some form of a decimal expansion.

This includes both rational numbers, which have a decimal expansion that either terminates or repeats, and irrational numbers, numbers that never terminate or repeat in their decimal expansion.

Answer 3

We found a few exceptions. The following are rational:

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 . . . . .

And also

-1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17, -18, -19, -20 . . . . .

Answer 4

Yes. Real numbers consist of all the rationals and all the irrationals.

Answer 5

Yes, as for example the square root of 2 is a real number but it is an irrational number that can't be expressed as a fraction.

Answer 6

Yes
Yes.

Answer 7

yes

Answer 8

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