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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.
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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, 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.
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Is an irrational number a real number?
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.
Is it true that all irrational numbers are real numbers?
Yes.
What is the set of numbers that includes all rational and all irrational numbers?
the set of real numbers
True or false irrational numbers are not real numbers?
False. Irrational numbers are real numbers.
What is the set of all rational and irrational numbers called?
Real numbers
If a number is a real number then is it also an irrational number?
No. All irrational numbers are real, not all real numbers are irrational.
Are all irrational numbers real number?
All irrational numbers are real, but not all real numbers are irrational.
All rational and irrational numbers are?
All rational and irrational numbers are real numbers.
Is this ture that all irrational numbers are real numbers?
Ye it is true that all irrational numbers are real numbers that can't be expressed as fractions.
Is every irrational number also real?
Yes, every irrational number is also a real number. Real numbers include all the numbers on the number line, which consists of both rational and irrational numbers. Rational numbers can be expressed as fractions, whereas irrational numbers cannot be expressed as simple fractions. So, while all irrational numbers are real numbers, not all real numbers are irrational—some are rational.
Are all unreal numbers irrational?
No. Irrational numbers form a proper subset of real numbers. That means that all irrationals are real so non-reals cannot be irrational.
Why does a real number have to be rational or irrational?
Because irrational numbers are defined as all real numbers which are not rational.
Is every irrational number a real number and how?
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.
Can all real numbers be irrational?
Irrational numbers are real numbers because they are part of the number line.
Is the number 3 an integer rational irrational or a real number?
It is an integer. All integers are rational but not irrational. All rational and irrational numbers are real numbers.
How are rational and irrational numbers alike?
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.
Is all irrational numbers real numbers?
Yes.
