Relations and Functions - Revision history

Suhridk: /* Sequences */

2012-02-15T16:08:05Z

Sequences

2012-02-15T16:05:52Z

Sequences

2012-02-15T16:03:01Z

Sequences

2012-02-15T16:01:36Z

Sequences

2012-02-15T15:49:30Z

Sequences

2012-02-15T15:42:27Z

Functions

2012-02-14T15:53:40Z

Functions

2012-02-09T23:40:51Z

Relations

2012-02-09T20:23:08Z

Relations

2012-02-06T18:36:15Z

Created page with "= Relations = = Functions ="

New page

= Relations =

= Functions =

@@ Line 32: / Line 32: @@
 * Sequences may have repeated elements.
 * To specify that a sequence has distinct elements use iseq
-* Also written as s == <b, x, m>. b is in 1st pos, x in 2nd, m in 3rd.
+* Also written as s == <g, x, p>. g is in 1st pos, x in 2nd, p in 3rd.

← Older revision		Revision as of 16:05, 15 February 2012
Line 32:		Line 32:
	* Sequences may have repeated elements.		* Sequences may have repeated elements.
	* To specify that a sequence has distinct elements use iseq		* To specify that a sequence has distinct elements use iseq
		+	* Also written as s == <b, x, m>. b is in 1st pos, x in 2nd, m in 3rd.

← Older revision		Revision as of 16:03, 15 February 2012
Line 29:		Line 29:
	** Is shorthand for s: N ⟶ PERSON		** Is shorthand for s: N ⟶ PERSON
	** Together with the restriction, dom s = 1..#s		** Together with the restriction, dom s = 1..#s
		+	* By default a sequence includes null. To exclude null from a sequence use seq₁
		+	* Sequences may have repeated elements.
		+	* To specify that a sequence has distinct elements use iseq

@@ Line 24: / Line 24: @@
 * A sequence is a specialised sort of function.
-* It is a partial function which maps numbers to elements.
+* It is a '''partial function''' which maps numbers to elements.
 * Sequence starts from 1 and are consecutive.

← Older revision		Revision as of 15:49, 15 February 2012
Line 22:		Line 22:

	= Sequences =		= Sequences =
		+
		+	* A sequence is a specialised sort of function.
		+	* It is a partial function which maps numbers to elements.
		+	* Sequence starts from 1 and are consecutive.

← Older revision		Revision as of 15:42, 15 February 2012
Line 20:		Line 20:
	** Total surjective is where all sources are mapped and all targets are. (There can be converging arrows).		** Total surjective is where all sources are mapped and all targets are. (There can be converging arrows).
	* A bijective function is one a function which is an injection, a surjection and is total.		* A bijective function is one a function which is an injection, a surjection and is total.
		+
		+	= Sequences =

← Older revision		Revision as of 15:53, 14 February 2012
Line 9:		Line 9:

	= Functions =		= Functions =
		+
		+	* A function is a relation where a single element cannot be mapped to more than one element. No two maplets with the same source. No diverging arrows.
		+	* A partial function is where not all the source elements are mapped to a target.
		+	* A total function is where all the source elements are mapped to a separate target. (Note, all the targets need not be used).
		+	* An injective function is where the target elements of the maplet dont have multiple sources. No converging arrows.
		+	** Partial injective : No converging arrows for a target and not all sources are mapped to a target.
		+	** Total injective: No converging arrows for a target and all sources are mapped to a target.
		+	* Surjective function is where all the target elements are mapped by the function.
		+	** Partial surjective is where all sources are not mapped but all targets are.
		+	** Total surjective is where all sources are mapped and all targets are. (There can be converging arrows).
		+	* A bijective function is one a function which is an injection, a surjection and is total.

@@ Line 6: / Line 6: @@
 * A binary relation between A and B is '''any subset of A X B'''.
 * Thus a relation R is given by R: P(A X B). R is a member of the powerset of the cartesian product of A and B.
 = Functions =

← Older revision		Revision as of 20:23, 9 February 2012
Line 1:		Line 1:
	= Relations =		= Relations =

		+	* An ordered pair (a,b) consists of two elements.
		+	* In Z, ordered pairs are represented using the maplet notation: a ⟼ b
		+	* The cartesian product, A X B is the set of all ordered pairs of A and B.
		+	* A binary relation between A and B is '''any subset of A X B'''.
		+	* Thus a relation R is given by R: P(A X B). R is a member of the powerset of the cartesian product of A and B.

	= Functions =		= Functions =