Frank Lonegro
3/21/14
Disc. Struct. 220
Hicks
Word Count
Mathematics has existed ever since humans were brought into life and has only evolved
through time. But, many people have asked: Is math real? Well, math is not real in the sense that
you can touch

Frank Lonegro
Discrete Structures
Hicks
11/30/13
Word Count 1,388
3-D Printing: A Practical Activity of Mathematics
Mathematics is involved in everyday society ranging from thousands of years ago to the
present day and will only continue to evolve as the

3-D Printing
A Relative Application of Mathematics
Frank Lonegro
A paper presented for
Discrete Structures
Mathematics Department
Howard Community College
United States
April 28, 2014
1
Introduction
Mathematics has existed ever since humans were brought i

Works Cited
Anderson, Chris. Makers: The New Industrial Revolution. New York: Crown Business, 2012.
Print.
Euchner, Jim. "The uses and risks of open innovation: user innovation is a more radical approach
to open innovation that can challenge the fundament

1. The difference of any two odd integers is even. (true)
Let n = 2p + 1 and m = 2q + 1 be two arbitrary odd integers.
Then n m = 2p 2q = 2(p q) is even.
2. By definition, a rational number can be expressed as a fraction with integer values in the
numerat

Question1.
1. All programmers enjoy discrete mathematics
x P(x)->P(y) cfw_P(x) is programmer and P(y) is enjoying discrete mathematics
2. Some integers are not odd
x P(x) cfw_xW P(x) is even integer
3. Every integer that is divisible by 2 is even
x D(x)->