What is a real number (also rational, decimal, integer, natural ...
In mathematics, there seem to be a lot of different types of numbers. What exactly are: Real numbers Integers Rational numbers Decimals Complex numbers Natural numbers Cardinals Ordinals And as …
Definition (s) of rational numbers - Mathematics Stack Exchange
The definitions of rational numbers are somewhat confusing for me. The definition of rational numbers on wikipedia and most other sites is: In mathematics, a rational number is any number that c...
proof of rational numbers as repeating or terminating decimal
Therefore every rational number is represented by a decimal that either terminates or repeats. Formal proof attempt: Claim: if a number is rational, then it's decimal expansion either terminates or repeats. …
Are there real numbers that are neither rational nor irrational ...
Sep 15, 2015 · However, if you think about algebraic numbers, which are rational numbers and irrational numbers which can be expressed as roots of polynomials with integer coefficients (like 2–√ 2 or …
How can I prove that all rational numbers are either terminating ...
Sep 5, 2011 · I am trying to figure out how to prove that all rational numbers are either terminating decimal or repeating decimal numerals, but I am having a great difficulty in doing so. Any help will be …
radicals - What rational numbers have rational square roots ...
25 All rational numbers have the fraction form a b, where a and b are integers (b ≠ 0). My question is: for what a and b does the fraction have rational square root? The simple answer would be when both …
Difference between rational numbers and fractions
Dec 14, 2025 · What's the difference between a fraction and a rational number? What's the clear cut boundary line that makes a fraction a fraction? As per my understanding rational numbers can be …
Produce an explicit bijection between rationals and naturals
Oct 24, 2010 · I remember my professor in college challenging me with this question, which I failed to answer satisfactorily: I know there exists a bijection between the rational numbers and the natural …
Rational + irrational = always irrational? - Mathematics Stack Exchange
Oct 29, 2013 · I had a little back and forth with my logic professor earlier today about proving a number is irrational. I proposed that 1 + an irrational number is always irrational, thus if I could prove that 1 +
Why is $\\mathbb Q $ (rational numbers) countable?
Feb 6, 2015 · In fact, this is not the function used to count rational numbers. Imagine listing all of those numbers excluding the ones in which the fraction can be simplified. A possible bijection could be that …