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

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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).

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)

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)

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............)}

R= real numbers

Q= rational numbers

N= natural numbers

Z= integers

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

**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.

**R**= Real number

**Q**= Rational number

**N**= Natural number

**Z**= Integer

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