Discrete Mathematics. Discrete means apart distinct away from each other not continuous. Examples:. The (sound) pitch of a violin is continuous. The (sound) pitch of a piano is discrete. An electric analogue clock shows continuous time. A digital clock shows discrete time .
The (sound) pitch of a violin is continuous.
The (sound) pitch of a piano is discrete.
A digital clock shows discrete time.
A conventional photograph shows almost continuous shades of color.
A digital picture shows discrete shades of color
Subsets of the Real numbers
A subset of real numbers is said to be discrete if every member in the subset has a neighborhood that separates it from all other members in the subset.
For example, the above set (indicated by red dots) is discrete (click to see the “private” neighborhoods.
On the other hand, the set of fractions between 0 and 1 is not discrete.
It is clear that every finite subset of the real number is discrete. But there are infinite discrete subsets as well, such as the set of integers.
Therefore, finite mathematics is a part of discrete mathematics. But discrete mathematics contains more than just finite mathematics.
In order to study discrete mathematics and understand computer programming, one must have some basic knowledge of mathematical logic.
Hence in any beginning course of discrete mathematics, about 50% of the time is spent on mathematical logic.
A proposition cannot have free variables.
Propositional calculus is analogous to Arithmetic where we do not deal with variables
Predicate calculus on the other hand is analogous to Algebra, which is more complex than arithmetic but it requires the knowledge of arithmetic.
Note: a proposition is also called a statement.
Determine whether each of the following is a proposition:
1. Washington, D.C., is the capital of USA.
2. Please read this carefully.
3. All Martians like pepperoni on their pizza.
4. Jane forgot to bring her umbrella.
5. Would you please pass me the salt?