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Relations

1.3 Introduction to Functions

Different Types of Relations

  • Below are four types of possible relations:

a) One-to-one

Precalculus Concepts: One-to-One - Expii

b) One-to-many

one-to-many - Wiktionary

c) Many-to-one

Function Definition and Many-to-One, One to One Examples - YouTube

d) Many-to-many

Is this a partial non injective non surjective function? - Mathematics Stack Exchange
  • The interpretation is quite straightforward.

a) One-to-one relations means that for every element in the domain set (or simply every value of x), there is one and only one corresponding element in the range (as in, one corresponding y).

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1.2 Describing a Set and Function

Describing a Set

  • It is not always possible to list all the elements in a set (e.g. N, Z, Q, R as above). There is a way of describing sets that is useful for infinite sets (i.e. sets with an infinite number of elements).
  • The set of all x such that ____ is denoted as \left\{x:_{-----}\right\}. For example:

i) \{x:0<,\ x<1\} is the set of real numbers strictly between 0 and 1.

ii) \{x:x\leq3\} is the set of real numbers smaller or equal to 3.

iii) \{x: x>0, x \in Q\} is the set of all positive rational numbers.

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