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# Why we denote set of rational number by q?

Updated: 9/25/2023

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9y ago

Q stands for quotient. The letter R was already used for the set of Real numbers.

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7y ago

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Q: Why we denote set of rational number by q?
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### Why set of rational number is denoted by q?

In number systems Rational number is not represented just by q . they are represented in the form of p and q . P/q is rational number where q is not equal to zero.

### What is the symbol of a rational number?

The set of rational numbers is represented by Q.

### What letter is used to notate the set of a rational number?

&#8474; (fancy capital Q) is the set of rational numbers.

### Why is rational number denoted with q?

Probably, because Q denotes the set of rational numbers, which can formaly understood to be quotients of integers.

### How do you convert a decimal into a rational number?

Set the decimal in the form p/q, where p and q are integers.

### Can a rational number be positive?

a rational number is any number that can be expressed as p/q where p and q are both integers. Since integers can most definitely be positive-- you might know them as the set of Natural numbers-- then yes, a rational number can be positive.

### How do you write an irrational number in algebra?

There is no representation for irrational numbers: they are represented as real numbers that are not rational. The set of real numbers is R and set of rational numbers is Q so that the set of irrational numbers is the complement if Q in R.

### Why is the product of a non - zero rational number and an irrational number is irrational?

Let q be a non-zero rational and x be an irrational number.Suppose q*x = p where p is rational. Then x = p/q. Then, since the set of rational numbers is closed under division (by non-zero numbers), p/q is rational. But that means that x is rational, which contradicts x being irrational. Therefore the supposition that q*x is rational must be false ie the product of a non-zero rational and an irrational cannot be rational.

### What type of number can be written as a fraction p over q where p and q are integers and q is not equal to zero?

a rational number

### Why is one a rational number?

A rational number is a number which is in the form of P/Q and Q=!0 and P and Qshould be divisible by 1 .Hence,one is a rational number.

### What is a rational number and why?

A rational number is a number which can be expressed as a ratio of two integers, in the form p/q, where p and q are integers and q is not zero. it is so because that is how rational numbers are defined.

### The complement of the set of rational numbers?

Complement of a Set: The complement of a set, denoted A', is the set of all elements in the given universal set U that are not in A. In set- builder notation, A' = {x ∈ U : x ∉ A}. The Venn diagram for the complement of set A is shown below where the shaded region represents A'.Rational number, in arithmetic, a number that can be represented as the quotient p/q of two integers such that q ≠ 0. In addition to all the fractions, the set of rational numbers includes all the integers, each of which can be written as a quotient with the integer as the numerator and 1 as the denominator.Consider Q and Qc, the sets of rational and irrational numbers, respectively: x∈Q→x∉Qc, since a number cannot be both rational and irrational. So, the sets of rational and irrational numbers are complements of each other.