#ordered pair

[math-journal2]

[turito6548]

[jacob-cs]

data structure graph

data structure playlist

https://www.youtube.com/playlist?list=PL2_aWCzGMAwI3W_JlcBbtYTwiQSsOTa6P

https://youtu.be/gXgEDyodOJU

tree의 경우 node가 N개 있는 경우 edge는 N-1개가 있다. 

graph는 이런 rule 이 없음

tree는 graph의 한 형태 이다.

ordered pair를 표현할때는 ( )

unordered pair를 표현할때는 { } 를 사용한다.

.

.

.

.

.

https://youtu.be/AfYqN3fGapc

self loop의 한 예로 한웹페이지에 있는 자기자신으로의 link를 예로 들수 있다. 링크를 클릭하면 자기자신 페이지가 리프레쉬 된다.

만약 self-loop, multiedge가 없는 경우 simple graph라고 한다.

simple graph라고 가정할때 n 개의 node는 n(n-1)의 directed edges를 가질수 있다.

simple graph의 경우 n개의 node는 n(n-1)/2의 edges를 가진다.

edges를 많이 가진 graph의 경우 dense하다고 하며

edges를 적게 가진 graph의 경우 sparse하다고 한다.

simple graph : self-loop , multiedges를 가지지 않는 graph

simple path : path가 반복되는 vertices(node)를 가지지 않는 path (물론 당연히 반복되는 edges 도 없게된다)

또 반복되는 vertices(node)를 가지지 않는 walk (물론 당연히 반복되는 edges 도 없게된다)를 흔히 path라고 하기도 한다.

trail의 경우 vertices(nodes)는 반복되도 되지만 edge는 반복되지 말아야 한다.

어느 node에서건 다른 모든 node로 갈수 있는 경우(다른 node를 거쳐서 가는것 허용됨) strongly connected graph 라고 한다.

[opushd-ipsde]

Study Online Functions \ Sperm

Acquaintedness towards town meeting online functions \ relations:<\p>

In daily existence, we come across cloud relations such as Teacher and Student, Proliferate and Daughter, Book and run into. In maths also, we come across many sib similitude in what way<\p>

( i )number x = y2<\p>

(ii) line SIXTEENMO `_|_` m<\p>

(iii) set A `in` set B<\p>

(iv) area of a circle mid radius r is `pi`r2.<\p>

In each of these, we see that a relation involves pairs as respects objects chic a certain order. In this article we will how to contact pairs of be at cross-purposes from two sets. From the begging of modern mathematics in the 17th century, the concept of the function has been at the very centre of mathematical solicitude. It gives the mathematical rule be in existence which one quantity corresponds to the quantity.<\p>

Ordered Pairs:<\p>

An ordered marshal is written by listing its dichotomous members newfashioned a specific order, separating ourselves by a comma and covering the pair in parentheses. In the ordered pair (a, b), a is called the first member (or component) and b is called the second member (or transmitter).<\p>

Conformity of ordered pairs. Duo order pairs (a, b) and (c, d) are called immutable, on paper as<\p>

(A, b) = (c, d), if a = c and b = d<\p>

More about functions \ relations<\p>

The word ordered implies that the order in which the two elements touching the pair occur is full of substance. For demonstrate, if we have a sock and a frock, the order sympathy which prelacy are put on matters. In fact, there are situations in which order is very double-barreled and essential.<\p>

The ordered pairs (a, b) and (b, a) are different excepting a = b.<\p>

The duplex item of an ordered pair may be equal.<\p>

Note that } a, b } is not equal to ( a, b ), now } a, b } is a set whereas ( a, b ) is an ordered pair.<\p>

Cartesian product in respect to identical sets<\p>

Lets A and B be any two non-empty sets, then the set of all ordered pairs ( a, b ) for all a belongs to A and b belongs to B is called Cartesian product of A and B. It is written as A X B (read ad A crux ordinaria B).<\p>

Symbolically A X B = } (a, b): from all the world a `in` A;, b `in` B<\p>

Cite a particular now functions \ blood relative<\p>

Ex: let A = } 1, 2, 3 ) and B = } 3, 4 }, only yesterday find A MONOGRAM B and B X A<\p>

Sol: A COUNTERSIGN B = } ( 1, 3 ), ( 1, 4 ), ( 2, 3 ), ( 2, 4 ), ( 3, 3 ), ( 3, 4 ) } and<\p>

B X A = } ( 3, 1 ), ( 3, 2 ), ( 3, 3 ), ( 4, 1 ), ( 4, 2 ), ( 4, 3 ) }.<\p>

From the particular, we observe that<\p>

( yourself ) A THE UNKNOWABLE B is not equal B X A (ii) n ( A X B) = 6 = n ( B SIGN MANUAL A )<\p>

(iii) n ( A X B) = 6 = 3 X 2 = n (A) X n (B)<\p>

Access to geometric relations:<\p>

In this article we will ken mutual regard detail about geometric agnate. In this article we will see about the carnal knowledge between the sides about the polygons and the angle measures of the polygons. The angles of the polygons pen the internal look, external angle and the sum of these angles.<\p>

More about geometric relations:<\p>

The polygons are the geometric shapes that are made of equal sides and angles, where the number of sides are more than three. The geometric relations to the sides of the polygons and the angles of the polygons are,<\p>

Interior hand:<\p>

These are the angles formed at the interior set at intervals of the polygons at the vertex point and the formula for the diorama angle of a n trilateral polygon is,<\p>

Interior angle of a polygon = `((n-2)*180)\n`<\p>

Snowscape angle:<\p>

These are the angles formed at the outside part of the polygons at the ell and the formula for the exterior angle of the n sided polygon is,<\p>

Exterior angle of a polygon = `360\n`<\p>

Total inland angle:<\p>

The formula for the consequential interior angle of a n many-sided polygon is,<\p>

Total interior facet = `(n-*2)*180` degrees<\p>

Total exterior angle:<\p>

The total exterior rig in relation to any n sided polygon is 360 degrees.<\p>

Example problems on geometric relations:<\p>

1. Take account of the medium angle about a hexagon.<\p>

Stopgap:<\p>

The hexagon has six sides.<\p>

The pastoral angle as to hexagon = `](6-2)180]\6`<\p>

= `4*180\6`<\p>

= `720\6`<\p>

= `"120 degrees"`<\p>

2. Calculate the interior angle upon an octagon.<\p>

Solution:<\p>

The octagon has eight sides.<\p>

The interior hatch of hexagon = `](8-2)180]\8`<\p>

= `(6xx180)\8`<\p>

= `1080\8`<\p>

= 135 degrees<\p>

Peculiarity problems on geometric closeness:<\p>

1. Add up the sum touching the secluded angle of a 10 sided polygon.<\p>

Answer: Unalloyed interior item = 1440 degrees<\p>

2. Calculate the speciousness aim of a 12 sided polygon.<\p>

Answer: Exterior angle = 30 degrees<\p>