What do the letters R, Q, N, and Z mean in math?

Expert Answers
hala718 eNotes educator| Certified Educator

The letters R, Q, N, and Z refers to a set of numbers such that:

R = real numbers includes all real number [-inf, inf]

Q= rational numbers ( numbers written as ratio)

N = Natural numbers (all positive integers starting from 1. (1,2,3....inf)

z = integers ( all integers positive and negative ( -inf, ..., -2,-1,0,1,2....inf)


giorgiana1976 | Student

The letters R,Q,N,Z are the names of the set of the numbers, that have specific properties.

For instance, N is the letter which designates the set of natural numbers.

N = {0 , 1 , 2 , 3 ,............. , n ,.............}

If the set is N^*, that means that the 0 value does not belong to the set. We could also write as:

N^* = N - {0}

The letter Z designates the set of integer numbers, which contains positive and negative elements.

Z = {... , -n ,.... ,-4 ,-3 ,-2 ,-1 ,0 ,1 ,2 ,3 ,4 ,... ,n, .......}

So, the set Z is composed from the elements of N and their opposed.

The conclusion would be that N is a subset of Z.

Also Z^* = Z-{0}.

The letter Q designates the set of rational numbers. The set could be mathematically described as:

Q = {m/n / m and n belong to Z, m is not divided by m}.

So, Q is composed from elements, which are ratios, where the numerator is not divided by the denominator and both, numerator and denominator, are integer numbers.

The letter R designates the set of real numbers. This set includes all the elements from the sets described above. So, we could say that the sets N,Z,Q are the subsets of R.

In the set R appear the symbols: -infinite and +infinite.

The set R is described as an interval that is bounded by the symbols -infinite and +infinite. In this interval, between the 2 boundaries, are located all the real numbers.

R = (-infinite , +infinite)

adarshanurag | Student

The letters R, Q, N, and Z refers to a set of numbers ...........

R= {real numbers which include all rational and irrational numbers}

Q= {rational numbers}

N = {Natural numbers (starting from 1,2,3,4,5,..........)}

Z = {integers (...........-3,-2,-1,0,1,2,3,4............)}

neela | Student

Normally we  the letters R,Q,N and Z denote the set of numbers with characteristics as indicated below:

R , the set of all real numbers, containing all rational and irrational numbers. Q, N , Z are the subsets of the set R.

Q, the set of all rational numbers. The rational numbers are any number which could be written  like p/q, where p and q are integrs.

N is the set of all natural numbers like:1,2,3,4,5,....... The set has starting number 1 and the consecutive numbers  increments by 1 . It has no end.

Z is integers( positive  or negatives including  zero).

lucario | Student

Variables I think

ik9744 | Student

R= Real number

Q= Rational number

N= Natural number 

Z= Integer

rimmery | Student

R is for real numbers, rational or irrational (Ex. 3, -5/2, 3.14)

Q represents rational numbers, so all numbers that can be represented as a fraction. For example, pi is NOT a rational number, but whole numbers and decimals belong in Q.

N is the set of Natural Numbers. These are whole numbers that are GREATER THAN ZERO. Whether or not it includes 0 depends on the course/university I think. (0 doesn't count in my CS courses but it does in math)

Z is the set of integers, so whole numbers, both positive and negative. 

zumba96 | Student

R is usually referring to real numvbers

Q is usually is referring to the rational numbers

N is for the natural numbers and

Z is for integers

Yojana_Thapa | Student

R= real numbers

Q= rational numbers

 N= natural numbers 

Z= integers

gaya3gopalan | Student

Hi! Thank you for posting this question in enotes

Maths is a fascinating language. Like English language, Maths too has its set of own alphabets. They are known as symbols. First, the letters R, Q, Z, and N represent a set of numbers. Therefore, they are called as set notations.

In maths, R means the set of all real numbers. Real numbers are those numbers that exist well within the real world. These numbers include all the positive and negative integers, rational and irrational numbers and so on. Therefore, R is usually notated as R = (-∞, +∞). By doing so, we are saying R contains all possible numbers that are bound to exist in the real world. There are many people who denote R as R = [+∞, -∞]. Both the representations mean the same. As ∞ is often an excluded component in maths (you can neither define infinity nor you can measure it), I had chosen an open interval () representation.

Next, by the term Q you mean the set of all rational numbers. A rational number will always be of the form p/q, where q ≠0. Suppose if q was zero, then the whole term will turn into infinity, violating the definition of a rational number. That is the set Q includes all whole numbers and its fractional parts.

By the term Z, we mean the set of integers. Thus, Z includes all positive and negative numbers, but, do not include their fractional parts or decimal terms. Hence, Z can be written in set notation as

Z = {-3, -2, -1, 0, 1, 2, 3…}

Now, finally, N means the set of natural numbers. Those positive numbers excluding zero fall under this category. Thus, N = {1,2,3…}

That’s all! But, by now you would have noticed that one set always seems to be bigger than the other. That is, one set tends to contain the other. So, if you rearrange your representations in terms of their encompassing abilities, then you can see that

R (real numbers) > Q (rational numbers) > Z (integers) > N (natural number)

emmaoconnor4 | Student

what does 'n' or 'u' like letter between two letters in sets mean? eg. (MuN). 

antoniobushell5 | Student

N8 is 128 but n equals?