Is infinity rational?

Question

I know this question might be a little silly, since "infinity" might not be considered part of the set of real numbers. But if you did count it, would it be rational or irrational?

Answer 1

it is neither rational or irrational. It's a concept, an idea. It has no numerical value.



All rational and irrational numbers can be represented as a finite quantity, whereas infinity cannot.

Answer 2

Neither. Rationality is something that only applies to real numbers, and infinity is not a real number. Simply pretending it's a real number for the sake of this question doesn't work either. If infinity were rational, it could be written in the form a/b, where a and b are integers. But, no matter what a and b are, a/b will always be finite. So, you could say infinity is irrational. However, this screws up some basic facts about irrational numbers. For example, irrational numbers have non-terminating, non-repeating decimal expansions. However, the second you assume infinity has any kind of decimal expansion, you are fixing it into a unique representation involving digits, which makes it finite.

Answer 3

According to me infinity is considered as a largest number. So basically it must be a number may be this number is largest never ending number. So this is never ending number and irrational numbers are non terminating,and never ending numbers. So infinity should be treated as irrational number

Answer 4

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lim (√(9x²+x) -3x) multiply by (√(9x²+x) +3x)/(√(9x²+x)+3x) lim (√(9x²+x) -3x)(√(9x²+x) +3x)/(√(9x²+x)+3x) after a simplification: lim (x/(√(9x²+x)+3x) lim x / (√[x²(9+1/x)] +3x) lim x / [x√(9+1/x) +3x] lim x / x [√(9+1/x) +3] lim 1 / [√(9+1/x) +3] x→ ∞ so: lim 1 / [√(9+1/∞) +3 =>1/√9 +3 =>1/3+3 =>1/6 *the idea to factor the x in the square root is for to remove from the square root and then take x as a common factor in the denominator. by having x in the numerstor too then x cancel

Answer 5

neither



it isnt a really solid hard core number

just a concept

or idea of some sort

its like asking if aliens are real

its not proven nor disproven

just some idea brought up

Answer 6

It is not a number, so how can you even classify it

Answer 7

NO, IT IS IRRATIONAL. ONLY A FOOL WOULD CALL IT RATIONAL. AND I AM NO FOOL. >:(