integers less than or equal to -3?

Expert Answers
hala718 eNotes educator| Certified Educator

integers less than or equal to -3

or :

x =< -3


x = { -inf, ...., -6,-5,-4,-3}

giorgiana1976 | Student

All integers which are less or equal to 3 are the elements of the integer set, which is noted as Z.

The whole integer set Z is:

Z = {....., -n, .......... -5, -4, -3, -2,- 1, 0, 1, 2, 3, 4, 5, ........, n, .........}

Now, the set which is formed only form the integer elements that are less or equal to -3, is the subste of Z.

We could enunciate it mathematically as:

A = {x / x=<-3, x belongs to Z}

We'll read what's inside A in this way:

All the elements x, that have the property (/) that all are less or equal to -3 (x=<-3) and they are all integers (x belongs to Z).

Now, let's extract from the entire set Z, the subset A. We'll keep only the integer elements which are less or equal to -3.

A = {....., -n, ..........-6, -5, -4, -3}

Note: infinite is the element of the real numbers set and it's not included in the integer number set.

neela | Student

The integers less than  or equal to -3.

We can represent the integers less than or equal to -3 as below:

Set building method:

S = { x: x is any  integer  and x < = -3}

Set by listing method:

S = { -3,  -4,  -5,  -6,   -7,...........} where the negative numbers are in decreasing order the first or starting element is -3. There is no last element. The set is an infinite set.

Set  incresing order by listing method:

S = { .................., -6, -5, -4,  -3}. Not possible to identify the   first or 2nd element element. But there is the last element -3.