Let O represent the set of odd natural numbers less than 10. Represent 0 in set

Question

Explanation / Answer

FOLLOW THIS In other words any value greater than 0 Notes: The "x" is just a place-holder, it could be anything, such as { q | q > 0 } Some people use ":" instead of "|", so they would write { x : x > 0 } Type of Number It is also normal to show what type of number x is, like this: The means "a member of" (or simply "in") The is the special symbol for Real Numbers. So it says: "the set of all x's that are a member of the Real Numbers, such that x is greater than or equal to 3" In other words "all Real Numbers from 3 upwards" There are other ways we could have shown that: On the Number Line it looks like: In Interval notation it looks like: [3, +?) Number Types I showed you (the special symbol for Real Numbers). Here are the common number types: Natural Numbers Integers Rational Numbers Real Numbers Imaginary Numbers Complex Numbers Example: { k | k > 5 } "the set of all k's that are a member of the Integers, such that k is greater than 5" In other words all integers greater than 5. This could also be written {6, 7, 8, ... } { k | k > 5 } = {6, 7, 8, ... } Why Use It? If you have a simple set like the integers from 2 to 6 you could just write: {2, 3, 4, 5, 6} But how would you list the Real Numbers in the same interval? {2, 2.1, 2.01, 2.001, 2.0001, ... ??? So instead just say how to build the list: { x | x ? 2 and x ? 6 } Start with all Real Numbers, then limit them between 2 and 6 inclusive. You can also use set builder notation to do other things, like this: { x | x = x2 } = {0, 1} All Real Numbers such that x = x2 0 and 1 are the only cases where x = x2

Related Questions

Navigate

• Browse (All)
• Browse L
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.