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.
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.
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 . . . . .
Yes. Real numbers consist of all the rationals and all the irrationals.
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.
Yes
Yes.
yes
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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.
Yes.
the set of real numbers
False. Irrational numbers are real numbers.
Real numbers
No. All irrational numbers are real, not all real numbers are irrational.
All irrational numbers are real, but not all real numbers are irrational.
All rational and irrational numbers are real numbers.
Ye it is true that all irrational numbers are real numbers that can't be expressed as fractions.
Because irrational numbers are defined as all real numbers which are not rational.
No. Irrational numbers form a proper subset of real numbers. That means that all irrationals are real so non-reals cannot be 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.
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.
It is an integer. All integers are rational but not irrational. All rational and irrational numbers are real numbers.
Yes.
All real numbers are irrational. For example, Pi is an irrational number that is a real number. Other irrational numbers can be the square root of an imperfect square.