how many irrational numbers are present?
Answers
Answer:
There are infinite rational numbers between numbers.
For example between 4 and 5
You can write
4.856685369
49868686886
4.8383838
4.278283838 etc
Answer:
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Step-by-step explanation:
We know that the set of rationals, Q is dense in R. Then, Q+i where i is an irrational number (which is a subset of the set off all irrationals) is also dense in R (since R+i=R). Therefore, the set of irrationals is dense in R and there exists an irrational in every non-empty interval in R. As there are infinite (unaccountably) such intervals, there are infinite irrationals between and two
rational numbers.
Between any two numbers, however large or small the difference between them may be, we have infinite rational as well as irrational numbers. As such between 1 and 6 too we have infinite irrational numbers.
Irrational numbers in their decimal form are non-repeating and non-terminating numbers. Hence say between 1 and 1.01, we can construct infinite irrational numbers like 1.00001000100001......., 1.01001000200003.......
1.00002000200002........
1.00003000300003....... and so on.
Similarly, between any two rational numbers a and b, we can have a+b2, a rational number and then between a and a+b2 as well as a+b2 and b, we can construct more rational numbers. And repeating this we can have infinite rational numbers between any two rational numbers.
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