HallsofIvy said:If the uniqueness is the problem, then suppose there were two solutions, x1 and x2. Since they are solutions to that equation, you must have, of course, ax1+ b= c and ax2+ b= c. Subtracting one equation from the other, a(x1- x2)= 0. What does that tell you?
Discrete math is a branch of mathematics that deals with discrete, or distinct, objects rather than continuous ones. It is used to study mathematical structures that are countable, such as integers, graphs, and sets.
Discrete math is important because it provides the foundation for many other areas of mathematics, including computer science, cryptography, and theoretical physics. It is also used in various real-world applications, such as data analysis and optimization problems.
A proof in discrete math is a logical argument that shows the validity of a mathematical statement or theorem. It involves using axioms, definitions, and previously proven theorems to arrive at a conclusion that is supported by irrefutable reasoning.
Discrete math is different from calculus in that it deals with discrete, or countable, objects rather than continuous ones. It also focuses more on logical reasoning and proof techniques, rather than on numerical calculations and functions.
Some common applications of discrete math include computer algorithms, coding theory, network analysis, and operations research. It is also used in various fields of science, such as biology, chemistry, and physics, to model and analyze discrete systems and phenomena.