o
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The dots at the end tell us that the list of odd numbers continue indefinitely. E. g.: The set of odd natural numbers is represented by { 1, 3, 5, …}.
In roster form, an element is not generally repeated, i. e., all the elements are taken as distinct.
E. g. The set of letters forming the word‘ SCHOOL’ is { S, C, H, O, L }.
Set Builder Form
In set-builder form, all the elements of a set possess a single common property which is not possessed by any element outside the set.
o In the set { a, e, i, o, u }, all the elements possess a common property, namely, each of them is a vowel in the English alphabet, and no other letter possess this property.
Denoting this set by V, we write V = { x: x is a vowel in English alphabet }. o
Please note that any other symbol like the letters y, z, etc. could be used.
o The symbol should be followed by a colon“:”. o
o
After the sign of colon, we write the characteristic property possessed by the elements of the set and then enclose the whole description within braces.
If a set of number doesn’ t follow any pattern, it can’ t be written in set builder form.
More Example of set builder form o
A = { x: x is a natural number and 3 < x < 10 } is read as“ the set of all x such that x is a natural number and x lies between 3 and 10. Hence, the numbers 4, 5, 6, 7, 8 and 9 are the elements of the set A.
Numerical: Write the set { x: x is a positive integer and x < 4 } in the roster form.
Solution: Since the set has natural numbers less that 4, Set A ={ 1,2,3 }