Mathematical ideas are often divided into two types, those that are continuous, and those that are discrete.

An example of continuous is the number line. Between any two points, there are always more points.

For discrete sets, this is not true. For instance, in baseball there are four bases. If you get a hit it is either a one-base hit (what we call a single), a two-base hit, a three-base hit, or a home run. There is no such thing as a 2 1/2 base hit.

Discrete things are found in bundles or lumps, and you can only have certain numbers of them.

Money is another discrete idea because you can not sell anything for $0.005. Prices can be grouped for specials, like 2 for 99 cents, but if you buy one it is either 49 cents or 50 cents. Discrete does not mean it has to be whole numbers, but it does mean there are only some that can be chosen, and some can not.

Discrete sets can be infinite, but they can not be infinitely divisible. For example, the counting numbers from 1 to infinity are discrete, because, like the bases in baseball, you go from one to two and then to three but not the points in between. The number line from 0 to 1 is not discrete but continuous, because between any two points in the set, there is always another point. This is the key that makes the difference. In discrete we can talk about things that are "next to" each other, with nothing between them, while in continuous sets we cannot.

...atCS203 Homework 6
Section 9.1 Question 17 Solution: Show that the following identities hold. a) x ⊕ y = (x + y)(xy) b) x ⊕ y = (xy) + (xy) x 0 0 1 1 y 0 1 0 1 x⊕y 0 1 1 0 (x + y) 0 1 1 1 (xy) 1 1 1 0 (x + y)(xy) 0 1 1 0 (xy) 0 0 1 0 (xy) 0 1 0 0 (xy) + (xy) 0 1 1 0
Section 9.1 Question 20 Solution: Find the a) b) c) d) duals of the following Boolean expressions. x+y → xy xy → x+y xyz + xyz → (x + y + z)(x + y + z) xz + x · 0 + x · 1 → (x + z) · (x + 1) · (x + 0)
Section 9.1 Question 23 Solution: How many diﬀerent Boolean functions F (x, y, z) are there so that F (x, y, z) = F (x, y, z) for all values of the Boolean variables x, y, and z. The solution to this problem is to realize that by inverting the bits, the actual function is inverted. So for F (x, y, z) = F (x, y, z), then the ﬁrst four lines of the function must be an inversion (or mirror image) of the last four lines. So the number of possible combinations is 24 or 16, instead of 28 . x 0 0 0 0 1 1 1 1 y 0 0 1 1 0 0 1 1 z 0 1 0 1 0 1 0 1 x 1 1 1 1 0 0 0 0 y 1 1 0 0 1 1 0 0 z 1 0 1 0 1 0 1 0 (x + z) 0 1 0 1 1 1 1 1 (x + z) 1 1 1 1 1 0 1 0
Section 9.2 Question 3 Solution: Find the sum-of-products expansions of the following Boolean functions.
d)F (x, y, z) = x + y + z = x + y(x + x) + z(x + x) = x + xy + xy + xz + xz = x(z + z) + xy(z + z) + xy(z + z) + xz + xz 1
= xz + xz + xyz + xyz + xyz + xyz + xz + xz = xz(y + y) + xz(y + y) + xyz + xyz + xyz + xyz + xz(y + y) + xz(y + y) = xyz + xyz + xyz + xyz...

...numbers
C = the set of green numbers
D = the set of even numbers
E = the set of odd numbers
F = {1,2,3,4,5,6,7,8,9,10,11,12}
Answers:
AUB- {All BLACK and RED numbers}
A∩D- {All numbers that are both RED and EVEN}
B∩C- {NO numbers intersect between these two sets}
CUE- {All ODD numbers and 00, 0}
B∩F- {2,4,6,10,11}
E∩F- {1,3,5,7,9,11}
Part II: The implementation of the program that runs the game involves testing. One of the necessary tests is to see if the simulated spins are random. Create an n-ary relation, in table form, that depicts possible results of 10 trials of the game. Include the following results of the game:
Number
Color
Odd or even (note: 0 and 00 are considered neither even nor odd.)
Also include a primary key. What is the value of n in this n-ary relation?
The primary key is the trial attempts, the reason for this is because only one attempt can be linked to that trial attempt, therefore making it unique. The value of n is four.
Part III: Create a tree that models the following scenario. A player decides to play a maximum of 4 times, betting on red each time. The player will quit after losing twice. In the tree, any possible last plays will be an ending point of the tree. Branches of the tree should indicate the winning or losing, and how that affects whether a new play is made.
Part IV: (1) A gate with three rotating arms at waist height is used to...

...DISCRETEMATHEMATICSDiscretemathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly", the objects studied in discretemathematics – such as integers, graphs, and statements in logic – do not vary smoothly in this way, but have distinct, separated values.Discretemathematics therefore excludes topics in "continuous mathematics" such as calculus and analysis. Discrete objects can often be enumerated by integers. More formally, discretemathematics has been characterized as the branch of mathematics dealing with countable sets (sets that have the same cardinality as subsets of the integers, including rational numbers but not real numbers). However, there is no exact, universally agreed, definition of the term "discretemathematics." Indeed, discretemathematics is described less by what is included than by what is excluded: continuously varying quantities and related notions.
The set of objects studied in discretemathematics can be finite or infinite. The term finite mathematics is sometimes applied to parts of the field of...

... |Information and Communication Technology (KICT) |
|Department / Centre |Computer Science (CS) |
|Programme |Bachelor of Computer Science (BCS) |
|Name of Course / Mode |DiscreteMathematics |
|Course Code |CSC 1700 |
|Name (s) of Academic staff / |Assoc. Prof. Dr. Azeddine Messikh |
|Instructor(s) | |
|Rationale for the inclusion of the course|To introduce students DiscreteMathematics and its basic principles. |
|/ module in the programme | |
|Semester and Year Offered |Semester 1 and 2 |
|Status...

...brutality towards his beloved fellowmen. Rizal expresses his willingness to die for his motherland and bids goodbye to his love ones, his country and to all people whom he cared for. He wishes that the youth of today will continue what he had just started for the independence that he had fight for and he is also thankful of some Filipino’s who had just committed their lives for the love of their motherland. He never resented of putting his life in danger and was successfully executed his destiny which is to die for his country because of his determination and strong will of having reformation in political aspect for the equality between the Spaniards and the Filipinos. In his poem, he freed those words just to express what he had felt...ds. It was written in Fort Santiago a night before his execution at Luneta Park. That’s the reason why the poem is entitled “Mi Ultimo Adios” which literally mean My Last Farewell. This famous literary piece was written due to the given social situation where in he witnessed the slavery, cruelty and brutality towards his beloved fellowmen. Rizal expresses his willingness to die for his motherland and bids goodbye to his love ones, his country and to all people whom he cared for. He wishes that the youth of today will continue what he had just started for the independence that he had fight for and he is also thankful of some Filipino’s who had just committed their lives for the love of their...

...REFLECTIVE JOURNAL OF HANDOUT 1 ; WHAT IS THE PHILOSOPHY OF MATHEMATICS EDUCATION
According to the journal that written by Paul Ernest from University of Exeter that discuss mainly about the philosophy of Mathematics Education. After the presentation that had conducted by my friends about the topic and had been clarified by our lecturer my understanding about the philosophy in overall and specifically the philosophy inmathematics education. As reported by Paul Ernest in particular the philosophy is about systematic analysis and the critical examination of fundamental problems. He also reported that it involves the exercise of the mind and intellect that discover thought, inquiry, reasoning, and it’s the results, judgement, conclusions, and belief or beliefs. In the other statement he also mentioned that the philosophy is an area or activity that can be understood as its aims and rationale.
While the mathematics education is the activity or practice of teaching mathematics. Hence the philosophy of mathematics education that had been highlighted in this journal concern the aim or rationale behind the teaching of mathematics. As had been discussed in this journal the philosophy overall, the philosophy of mathematics and philosophy of Education have simply substantial entities in themselves but complex relationships and interactions between...

...Mathematics is defined as the science which deals with logic of shape, quantity and arrangement. During ancient times in Egypt, the Egyptians used maths and complex mathematic equations like geometry and algebra. That is how they managed to build the pyramids.
Our day today life would be quite strenuous without maths knowledge. There are many ways in which people use maths during the day today living. Below are some ways in which people use maths in daily lives.
* Daily life would be very difficult without maths’ knowledge at all. To begin with, you need to be able to organize and count your money; as well as subtract, divide and multiply. This is a skill everyone needs to have in order to survive. Every day we visit supermarkets to buy items, without maths knowledge, we would not be able to know if we have been given the right change.
* Some DIY jobs require basic maths knowledge for them to be done effectively. For example, a person needs to work out the amount of materials required in order to decorate a house. One has to be aware of the measurement, space and shape of the area he is working on to ensure that he or she has purchased the required amount of materials. This helps in ensuring that you do not run out of essential materials before the job is finished or you do not have too much left over.
* In the field of architecture or engineering, it is essential to have more advance maths knowledge. Working on geometry and algebra...

...History of mathematics
A proof from Euclid's Elements, widely considered the most influential textbook of all time.[1]
The area of study known as the history of mathematics is primarily an investigation into the origin of discoveries in mathematics and, to a lesser extent, an investigation into the mathematical methods and notation of the past.
Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments have come to light only in a few locales. The most ancient mathematical texts available arePlimpton 322 (Babylonian mathematics c. 1900 BC),[2] the Rhind Mathematical Papyrus (Egyptian mathematics c. 2000-1800 BC)[3] and the Moscow Mathematical Papyrus (Egyptian mathematics c. 1890 BC). All of these texts concern the so-calledPythagorean theorem, which seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry.
The study of mathematics as a subject in its own right begins in the 6th century BC with the Pythagoreans, who coined the term "mathematics" from the ancient Greekμάθημα (mathema), meaning "subject of instruction".[4]Greek mathematics greatly refined the methods (especially through the introduction of deductive reasoning andmathematical rigor in proofs) and expanded the subject matter of mathematics.[5] Chinese...