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Set notation
[[Category:Notation]] [[Category:Set theory]] ...math>\{red, green, blue, tope, mauve, \dots\}</math>. Be careful with this notation, for two reasons:

2 KB (317 words) - 19:31, 17 February 2018
Function notation
[[Category:Notation]] [[Category:Functions]]

<math>1 {{PLURAL:</math>1|byte|bytes}} (29 words) - 19:05, 17 February 2018
Sequence notation
We often want to prove that [[there exists]] a [[sequence notation|sequence]] of values <math>a_0, a_1, \dots, a_k</math>, all in <math>X</mat ...ether we allow [[finite]] or [[infinite]] sequences. I will only use this notation for [[finite]] sequences.

<math>1 {{PLURAL:</math>1|byte|bytes}} (173 words) - 15:24, 19 February 2020

Page text matches

CS 2800 Spring 2018
|1/29 || [[SP18:Lecture 3 Induction | More set notation, induction ]]

5 KB (608 words) - 16:55, 30 May 2018
FA17 Lecture 1
=== Set notation === {{:set notation}}

1 KB (171 words) - 18:37, 20 January 2018
Set notation
[[Category:Notation]] [[Category:Set theory]] ...math>\{red, green, blue, tope, mauve, \dots\}</math>. Be careful with this notation, for two reasons:

2 KB (317 words) - 19:31, 17 February 2018
FA17 Lecture 2
* new notation: cartesian product (<math>A \times B</math>), for all (<math>∀</math>), f == Notation ==

6 KB (1,139 words) - 13:24, 18 January 2018
FA17 Lecture 4
== Notation == '''Notation:''' if there is a sample space that is clear from context, I will write <ma

8 KB (1,388 words) - 13:25, 18 January 2018
FA17 Lecture 5
...>A|B</math> is not defined, only <math>Pr(A|B)</math>; this is an abuse of notation, but is standard.

4 KB (682 words) - 13:25, 18 January 2018
FA17 Lecture 9
'''Notation:''' In general, the set of functions with domain <math>A</math> and codomai

6 KB (1,154 words) - 13:28, 18 January 2018
∈
[[Category:Basic tools]] [[Category:Set theory]] [[Category:Notation]]

<math>1 {{PLURAL:</math>1|byte|bytes}} (55 words) - 13:07, 24 January 2020
Function notation
[[Category:Notation]] [[Category:Functions]]

<math>1 {{PLURAL:</math>1|byte|bytes}} (29 words) - 19:05, 17 February 2018
Set comprehension
[[Category:Set theory]] [[Category:Definition]] [[Category:Notation]] The notation [[Set comprehension|<math>\{x \mid \text{property of } x\}</math>]] denotes

1 KB (178 words) - 19:28, 17 February 2018
∅
...e> <noinclude> [[Category:Set theory]] </noinclude> <noinclude> [[Category:Notation]] </noinclude>

<math>1 {{PLURAL:</math>1|byte|bytes}} (35 words) - 12:59, 28 February 2018
RHS
[[Category:Notation]]

<math>1 {{PLURAL:</math>1|byte|bytes}} (22 words) - 19:24, 17 February 2018
⊆
...e> <noinclude> [[Category:Set theory]] </noinclude> <noinclude> [[Category:Notation]] </noinclude>

<math>1 {{PLURAL:</math>1|byte|bytes}} (47 words) - 14:16, 24 August 2018
❘
<noinclude>[[Category:Notation]] </noinclude> <noinclude> [[Category:Basic tools]] </noinclude> <noinclude

<math>1 {{PLURAL:</math>1|byte|bytes}} (131 words) - 14:24, 11 October 2018
ℕ
...<noinclude> [[Category:Number theory]] </noinclude> <noinclude>[[Category:Notation]] </noinclude>

<math>1 {{PLURAL:</math>1|byte|bytes}} (34 words) - 13:42, 21 February 2020
∪
...de> <noinclude> [[Category:Set theory]] </noinclude> <noinclude>[[Category:Notation]]</noinclude>

<math>1 {{PLURAL:</math>1|byte|bytes}} (33 words) - 13:00, 28 February 2018
∩
...de> <noinclude> [[Category:Set theory]] </noinclude> <noinclude>[[Category:Notation]] </noinclude>

<math>1 {{PLURAL:</math>1|byte|bytes}} (33 words) - 12:59, 28 February 2018
Definition
[[Category:Notation]]

<math>1 {{PLURAL:</math>1|byte|bytes}} (24 words) - 19:13, 17 February 2018
Integer
<noinclude>[[Category:Notation]]</noinclude> <noinclude> [[Category:Definition]] </noinclude> <noinclude>[

<math>1 {{PLURAL:</math>1|byte|bytes}} (33 words) - 11:58, 20 April 2018
2
[[Category:Notation]] [[Category:Set theory]] The notation <math>2^A</math> denotes the [[power set]] of A.

<math>1 {{PLURAL:</math>1|byte|bytes}} (16 words) - 18:51, 17 February 2018
WTS
[[Category:Proof techniques]] [[Category:Notation]]

<math>1 {{PLURAL:</math>1|byte|bytes}} (13 words) - 19:38, 17 February 2018
→
<noinclude>[[Category:Functions]] [[Category:Notation]]</noinclude> The notation <math>f : A → B</math> means "<math>f</math> is a [[function]] with [[dom

<math>1 {{PLURAL:</math>1|byte|bytes}} (41 words) - 13:14, 20 March 2020
∧
[[Category:Notation]] [[Category:Logic]]

<math>1 {{PLURAL:</math>1|byte|bytes}} (30 words) - 19:40, 17 February 2018
∨
[[Category:Notation]] [[Category:Logic]]

<math>1 {{PLURAL:</math>1|byte|bytes}} (28 words) - 19:40, 17 February 2018
∀
[[Category:Notation]] [[Category:Logic]]

<math>1 {{PLURAL:</math>1|byte|bytes}} (33 words) - 19:39, 17 February 2018
¬
[[Category:Notation]] [[Category:Logic]]

<math>1 {{PLURAL:</math>1|byte|bytes}} (24 words) - 15:23, 27 January 2020
∘
[[Category:Definition]] [[Category:Notation]] [[Category:Functions]]

<math>1 {{PLURAL:</math>1|byte|bytes}} (40 words) - 14:20, 15 September 2018
-1
<noinclude>[[Category:Definition]]</noinclude> <noinclude>[[Category:Notation]]</noinclude> <noinclude>[[Category:Functions]]</noinclude>

<math>1 {{PLURAL:</math>1|byte|bytes}} (50 words) - 12:33, 15 May 2018
Inductively defined set
=== BNF Notation ===

1 KB (181 words) - 11:35, 20 April 2018
⟦X→Y⟧ definition
...o I will use <math>[[⟦X→Y⟧]]</math> in the wiki. You may use either notation.

<math>1 {{PLURAL:</math>1|byte|bytes}} (70 words) - 17:13, 1 February 2019
XRy
<noinclude>[[Category:Relations]] [[Category:Notation]]</noinclude> Notation: If <math>R</math> is a [[binary relation]] on a [[set]] <math>A</math>, an

<math>1 {{PLURAL:</math>1|byte|bytes}} (64 words) - 14:26, 17 September 2018
Definition:Equivalence class
...⟦ and ⟧, but the wiki syntax makes this difficult. You may use either notation.

<math>1 {{PLURAL:</math>1|byte|bytes}} (101 words) - 15:29, 26 February 2020
Definition:Base b interpretation
...l]] <math>i</math>, then the [[base b interpretation]] of <math>[[Sequence notation|(d_i)]]</math>, written <math>(d_kd_{k-1}\cdots{}d_1d_0)_b</math> is given

<math>1 {{PLURAL:</math>1|byte|bytes}} (67 words) - 17:01, 8 October 2018
Definition:Base b representation
...git]]s, and if <math>a = (d_i)_b</math>, then we say that <math>[[Sequence notation|(d_i)]]</math> is [[Claim:the base b representation is unique|the]] [[Base

<math>1 {{PLURAL:</math>1|byte|bytes}} (57 words) - 17:02, 8 October 2018
Proof:Every natural number has a prime factorization
...th>[[sequence notation|(a_i)]]</math> and ending with the <math>[[Sequence notation|b_i]]</math>s (in other words, <math>c_0, c_1, \dots = a_0,a_1,\dots,a_p,b_

3 KB (437 words) - 12:16, 2 October 2018
Proof:Every natural number has a prime factorization (strengthened induction hypothesis)
...th>[[sequence notation|(a_i)]]</math> and ending with the <math>[[Sequence notation|b_i]]</math>s (in other words, <math>c_0, c_1, \dots = a_0,a_1,\dots,a_p,b_

4 KB (665 words) - 12:18, 2 October 2018
Sequence notation
We often want to prove that [[there exists]] a [[sequence notation|sequence]] of values <math>a_0, a_1, \dots, a_k</math>, all in <math>X</mat ...ether we allow [[finite]] or [[infinite]] sequences. I will only use this notation for [[finite]] sequences.

<math>1 {{PLURAL:</math>1|byte|bytes}} (173 words) - 15:24, 19 February 2020
Definition:Partition
# The <math>[[sequence notation|A_i]]</math> cover <math>A</math>, i.e. <math>A [[Equality (sets)|=]] A_1 [

<math>1 {{PLURAL:</math>1|byte|bytes}} (84 words) - 16:58, 2 October 2018
Base b representation
When we write down sequences of [[digit]]s in [[decimal]] (or [[base]] 10) notation, we interpret them according to a formula. For example, we interpret the n

1 KB (220 words) - 17:03, 8 October 2018
Decimal
No special notation is needed to indicate [[decimal]], since that's how we normally interpret n

<math>1 {{PLURAL:</math>1|byte|bytes}} (56 words) - 17:05, 8 October 2018
Octal
...nly used. Some programming languages allow you to write a number in octal notation by prefixing it with a 0 as in "0172" which (in some contexts) would be int

<math>1 {{PLURAL:</math>1|byte|bytes}} (55 words) - 17:07, 8 October 2018
Claim:Base b representation
...math> and <math>b > 0</math>, [[there exists]] a sequence <math>[[sequence notation|(d_i)]]</math> of [[digit]]s satisfying <math>a = [[base|(d_i)_b]]</math>.

<math>1 {{PLURAL:</math>1|byte|bytes}} (34 words) - 17:12, 8 October 2018
Proof:Base b representation
...(a,b)</math> and <math>r := [[rem]](a,b)</math>. [[Let]] <math>[[sequence notation|(d_i)']]</math> be the [[base b representation]] of <math>q</math> (which w

2 KB (347 words) - 12:48, 21 February 2020
Claim:The base b representation is unique
...ath>d_k' \neq 0</math> then <math>[[sequence notation|(d_i)]] = [[sequence notation|(d_i')]]</math>.

<math>1 {{PLURAL:</math>1|byte|bytes}} (113 words) - 17:14, 8 October 2018
↛
[[Category:Notation]]

<math>1 {{PLURAL:</math>1|byte|bytes}} (36 words) - 09:43, 13 September 2019
Example:Tricky set comprehension membership
Note that [[set comprehension]] notation can sometimes be tricky. Just because <math>x ∈ [[Set comprehension|\{x

<math>1 {{PLURAL:</math>1|byte|bytes}} (57 words) - 13:12, 24 January 2020
∃
<noinclude>[[Category:Notation]]</noinclude>

<math>1 {{PLURAL:</math>1|byte|bytes}} (17 words) - 16:12, 29 January 2020
Variants of induction
...ent to weak induction|change of variables]], but it occasionally makes the notation a bit easier to work with.

1 KB (196 words) - 13:39, 19 February 2020
Delta hat
<noinclude>[[Category:Notation]]</noinclude>

<math>1 {{PLURAL:</math>1|byte|bytes}} (45 words) - 10:01, 10 April 2020