- #1
jakey140
- 2
- 0
Is the number 1, or any other whole/negative number a rational number?
Rational Numbers: Is 1 a Rational Number?
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Discussion Overview
The discussion centers on the classification of the number 1 and other integers as rational numbers, as well as the rationality of square roots, particularly the square root of 13. The scope includes definitions, properties of numbers, and examples related to rational and irrational numbers.
Discussion Character
- Conceptual clarification
- Debate/contested
- Mathematical reasoning
Main Points Raised
- Some participants assert that every integer is a rational number because it can be expressed as a fraction (e.g., a = a / 1).
- There is a question about whether both positive and negative integers, as well as fractions, are classified as rational numbers.
- One participant proposes that the square root of any non-perfect square number is irrational, while suggesting that the square root of certain powers might be rational.
- Another participant states that the square root of 13 is irrational and provides a condition for when square roots are rational.
- A definition of a rational number is provided, emphasizing that it can be expressed as a fraction p/q, with p and q being integers and q not equal to 0.
- There is a suggestion to look up the definition of a rational number for further clarity.
Areas of Agreement / Disagreement
Participants generally agree that integers are rational numbers, but there is disagreement regarding the rationality of the square root of 13, with some asserting it is irrational and others discussing conditions under which square roots can be rational.
Contextual Notes
The discussion includes various assumptions about the properties of numbers and the definitions of rationality, which may not be universally agreed upon. The exploration of square roots and their classifications introduces additional complexity that remains unresolved.
- #2
radou
Homework Helper
- 3,149
- 8
Every integer is a rational number, since for every integer a you can write a = a / 1. The set of integers is a subset of the set of rational numbers.
- #3
jakey140
- 2
- 0
Alright thanks a lot =).. so both negative and positive intgers are rational, also any fraction?... would the square root of 13 be classified as rational?
- #4
radou
Homework Helper
- 3,149
- 8
Find the definition of a rational number on the internet (or on this forum), it will clear some things up. 
- #5
fourier jr
- 764
- 13
i think the square root of any number that isn't a perfect square is irrational... maybe the square root of any power whose exponent is a power of 2 is rational. the square root of a prime is irrational for sure, & i think that can be proven the same way the square root of 2 is proven irrational.
- #6
shmoe
Science Advisor
Homework Helper
- 1,971
- 2
the square root of 13 is irrational. For a natural number n, sqrt(n) is rational if and only if n=m^2 for some natural number m.
Similar statement for kth roots, n^(1/k) is rational if and only if n=m^k.
Similar statement for kth roots, n^(1/k) is rational if and only if n=m^k.
- #7
kar
- 1
- 0
The definition of a rational number is: a number that can be expresed as a fraction p/q, where p and q are integers, q is not equal to 0.
Thus, any integer (positive and negative) is a rational number.
As for sqrt(13) - you can try and prove that it is not a rational number.
Thus, any integer (positive and negative) is a rational number.
As for sqrt(13) - you can try and prove that it is not a rational number.
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