MMW MIDTERMS RN

Symmetry.

This is an exact correspondence of form and constituent configuration on opposite sides of a dividing line or plane or about a center or an axis.

Reflection Symmetry.

It is also called mirror symmetry or line symmetry.

Rotational Symmetry.

It is also called radial symmetry. In Biology, this kind of symmetry is exhibited by objects when their similar parts are regularly arranged around a central axis and the pattern looks the same after a certain amount of rotation.

Translational Symmetry.

This kind of symmetry is exhibited by objects which do not change its size and shape even if it moved to another location.

Fractals.

These are never-ending patterns that are self-similar across different

scales.

Spirals.

These are curved patterns made by series of circular shapes revolving around a central point.

Spots and stripes

Patterns are also exhibited in the external appearances of animals.

The Fibonacci sequence

is an integer in the infinite sequence 0, 1, 1, 2, 3, 5, 8,

13...The sequence begins with zero or one.

Language

facilitates communication and meaning-making. It allows people to express themselves and maintain their identity.

Mathematical Language

is the system used to communicate mathematical ideas.

Mathematics as a language

a system of communication about objects like numbers, variables, sets, operations, functions, and equations.

Precise

The mathematical language is precise. It is exact and accurate. It can make fine distinctions.

Concise

it prefers brevity. It is being able to say things briefly.

Powerful

can express complex thoughts with relative ease. It can convey its message and intended meaning effectively.

Convention

is a set of facts, rules or notations that are agreed upon or accepted to be the norm.

Set Notation

It is a system of marks, signs, figures, or characters that is used to represent information. A set may be specified using set-roster notation by writing all the elements between braces.

empty set or null set

A set that has no element is called the ________ ________ and is denoted by Ø or { }.

Set Roster Notation

is used to represent a set by listing each element of the set inside a pair of braces.

Set Builder Notation

is another way of defining a set by describing its elements.

Cardinality of Set

The cardinality or the cardinal number of a finite set is the number of elements in the set.

TYPE OF SET

• FINITE AND INFINITE SET

• EQUAL AND EQUIVALENT SET

• SUBSET AND PROPER SUBSET

• UNIVERSAL SET

Finite Set

A set is said to be finite if the number of elements can be counted.

Infinite set

uncountable or unlimited

Equivalent Sets

[1234] [abcd]

Subset

A= {1,2,3}  and    B={1,2,3,4,5,6,7,8}     we say that A c B.

Equal Set

[abcd] [dcba]

Proper Subsets

a proper subset is a subset which contains fewer elements of its parent set

Mathematical reasoning

is the bedrock upon which the entire discipline of mathematics is built.

Inductive Reasoning

It is the process of making general conclusions based on specific examples

Deductive Reasoning

It is the process of making specific conclusions based on general statement