The document is an introduction to mathematical concepts, specifically focusing on angles, triangles, parallel lines, and basic proofs. It explains terms like right angles, the Frobenius inner product, and the ellipsis used in mathematical lists and representations. Examples are provided to illustrate how these concepts apply in mathematical reasoning and proofs.

1. 5th Lesson Introduction to Math.
Ishik University
∟‖ ∴… ∵ : ∠
Faculty of Education
Physics Department
Instructed and Prepared by: Sivar A. B.

2.  Used over an amount to show that this is an angle
 Example:
 A triangle of equal side with angle ∠ 60 of on of the
sides.

 Means that the angles ∠ ABC=∠CAB ∠BCA=30̊
∠ Degree
A B
C

3.  A triangle with one of the angles right , means that
 A =∟ Right angle =90 ̊ means ∠BAC= 90 ̊
∟ Right angle
A
B
C

4.  When two of the sides are parallel to each other
means the angle between these sides are zero degree
 *(0̊ )
 1- so A and D are parallel means that the angle
between them is zero degree (0̊ ) so A ‖ C, as well as
 B ‖ D
‖ Parallel to
A
B
C
D
z

5.  A : B means the Frobenius inner product of the
matrices A and B.
 A : B means the division of A with B (dividing A by B)
10 : 2 (ten to two) = 5
: Is to or ratio

6. ∴ therefore, so and hence
 Sometimes used in proofs before logical
consequences.
Example:
 A ‖ D and D ‖ E ∴ A ‖ E
A
B
C
D E

7.  Sometimes used in proofs before reasoning.
 Example:
 x + y = 6
 ∵ x =1
 ∴ x+y=1+y=6
 y= 6-1=5
∵ Since or Because

8.  An ellipsis is also often used in mathematics to mean
"and so forth". In a list, between commas, or
following a comma, a normal ellipsis is used, as in:
 1,2,3, …,100.
 N is a normal set of number
 N={0,1,2, …, ∞}
… ellipsis or etc.