Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [discrete-mathematics]

The study of discrete mathematical structures. Consider using a more specific tag instead, such as: (combinatorics), (graph-theory), (computer-science), (probability), (elementary-set-theory), (induction), (recurrence-relations), etc.

Discrete mathematics is not the name of a branch of mathematics, like number theory, algebra, calculus, etc. Rather, it's a description of a set of branches of math that all have in common the feature that they are "discrete" rather than "continuous".

The term "discrete mathematics" is therefore used in contrast with "continuous mathematics," which is the branch of mathematics dealing with objects that can vary smoothly (and which includes, for example, calculus). Whereas discrete objects can often be characterized by integers, continuous objects require real numbers.

Though there cannot be a definite number of branches of Discrete Mathematics, the following topics are almost always covered in any study regarding this matter −

  • Sets, Relations and Functions
  • Mathematical Logic
  • Group theory
  • Counting Theory
  • Probability
  • Mathematical Induction and Recurrence Relations
  • Graph Theory
  • Trees
  • Boolean Algebra

For an overview, see the Wikipedia entry on Discrete mathematics.

and http://www.cs.yale.edu/homes/aspnes/classes/202/notes.pdf

Consider using a more specific tag instead, such as: , , , , , , , , etc.

32903 questions
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Math induction sum of even numbers

I need to prove by induction this thing: $2+4+6+........+2n = n(n+1)$ so, this thing is composed by sum of pair numbers, so its what I do, but I'm stucked. $2+4+6+\cdots+2n = n(n+1)$ $(2+4+6+\cdots+2n)+(2n+2) = n(n+1) + (2n+2) $ $n(n+1)+(2n+2) =…
PlayMa256
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Prove that $\lfloor an \rfloor +\lfloor (1-a)n \rfloor = n-1 $

Given and irrational $a$ and a natural number $n$ prove that $\lfloor an \rfloor +\lfloor (1-a)n \rfloor = n-1 $. Is this solution correct? $\lfloor an \rfloor +\lfloor (1-a)n \rfloor = \lfloor an \rfloor +\lfloor n-na \rfloor =$ (we take out $…
Arek Krawczyk
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How to prove that if $2x^2-x=2y^2-y$, then $x=y$, for $x,y\in\mathbb{Z}.$

How to prove that if $2x^2-x=2y^2-y$, then $x=y$, for $x,y\in\mathbb{Z}.$
Jam
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How many regions do $n$ lines divide the plane into?

Suppose you draw $n \ge 0$ distinct lines in the plane, one after another, none of the lines parallel to any other and no three lines intersecting at a common point. The plane will, as a result, be divided into how many different regions $L_n$? Find…
nodebase
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If n be a positive integer, then prove by binomial theorem that the integral part of $(7+4\sqrt3)^n$ is an odd number.

I wanted to know, how can i prove this? If $n$ be a positive integer, then prove by binomial theorem that the integral part of $(7+4\sqrt3)^n$ is an odd number.
Shobhit
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A wheel has the numbers 1 to 25 randomly placed on it. Show that there are three adjacent numbers whose sum is at least 39.

Any thoughts on understanding how to do this using the Principle of Mathematical Induction would be great. A wheel of fortune has the integers from 1 to 25 placed on it in a random manner. Show that regardless of how the numbers are positioned on…
dwinget2008
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SUPPOSE versus IF

What is the difference between suppose . . ., then . . . and if . . ., then . . . ? For instance, in this... "Let P(n) be a statement that is defined for all nEZ and let a be a fixed integer. Suppose that both of the following statements are…
user888449
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Two identity element?

On $\Bbb N=\{0,1,2,...\}$ we define the operation $\otimes$ by $m\otimes n= |m-n|$. Are there any identity element? I came up with two identity elements. $e= 0$ and $e=2m$ for an element $m$ in the set, but how is that possible? I thought on a…
Erika
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Having extreme difficulty understanding conditional statements.

everyone. I'm having a very difficult time understanding conditional statements, and was hoping someone could help me understand them. I took discrete math this last spring and remember struggling with them, but at some point had to let go and just…
GainzNerd
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Show that, if $f:A\to B$ is a function, with $A$ and $B$ being finite sets, and $|A|=|B|$, then $f$ is one to one iff $f$ is onto.

I'm a little stuck with this proof. Not sure where to go. I was thinking that I could first assume that $f$ is one to one and prove that it's onto, and then assume it's onto and prove that it's one to one... but I'm not sure what to do with the…
Mirrana
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Vertices and edges of a cube are assigned natural numbers in a particular way; can the sum of the vertices equal the sum of the edges?

At the vertices of a cube are written 8 different natural numbers, and on each of its edges is written the greatest common divisor of the numbers at the endpoints of the edge. Can the sum of the numbers written at the vertices be the same as the…
ANONYMOUS
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Assume that $k$ is a particular integer. Is $2k − 1$ odd?

Hello I'm having trouble wrapping my head around how $2k-1$ is odd. My solution shows this: Yes $2k-1$ is odd! $2k − 1 = 2(k − 1) +1$ and $k − 1$ is an integer because it is a difference of integers. This is my understanding. An odd number is…
Jlee
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Question about divisibility by $3$

Lets assume that for every $x,y,z$ that belong to an $A$ , $(x+2y)$ and $(y+2z)$ can be divided by $3$.If we want to prove that $(x+2z)$ can also be divided by $3$, is it ok to do the next steps ? $(x+2y),(y+2z)$ can be divided by $3$, so lets take…
p0ffer
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Is it possible to create a function that's onto but not 1-1 between two sets with the same cardinality?

Given two sets, $S = \{1, 2, 3\}$ and $T = \{a, b, c\}$ is it possible to create a function $F:S\rightarrow T$ that is onto but not one to one? It seems like the only way to do this would be not to use all the elements in $S$, but then it wouldn't…
Zaya
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Distance between a real number and a whole number

Prove that if $a$ is real and $n$ natural. The distance between one of the numbers $a,2a,3a,...,na$ and a whole number is at most $\frac{1}{n}$. This is a problem from discrete math, but hints from analysis would be appreciated.
yolo expectz
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