There are different sizes of infinity. For example, the set of all real numbers (including fractions and irrational numbers) is infinitely larger than the set of counting numbers (1, 2, 3, ...).
Infinite Numbers:
The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding ones.
Fibonacci Sequence:
This triangular array of binomial coefficients has numerous properties and applications in combinatorics, probability theory, and algebraic expressions.
Pascal's Triangle:
Prime numbers are integers greater than 1 that have no positive divisors other than 1 and themselves.
Prime Numbers:
Pi is the ratio of the circumference of a circle to its diameter and is approximately equal to 3.14159. It is an irrational number, meaning it cannot be expressed as a finite decimal or fraction.
Pi (π):
The concept of zero as a placeholder and a number in its own right was invented independently by different cultures. It revolutionized mathematics by allowing for more sophisticated calculations and paved the way for modern algebra and calculus.
Zero:
They are used extensively in fields such as electrical engineering, quantum mechanics, and signal processing.
Imaginary Numbers:
The Butterfly Effect is a concept from chaos theory, which suggests that small changes in initial conditions can lead to vastly different outcomes in complex systems.
The Butterfly Effect:
Fractals are complex geometric shapes that exhibit self-similarity at different scales. They are found abundantly in nature, such as in coastlines, snowflakes, and the branching patterns of trees, and have applications in computer graphics and modeling.
Fractals:
Game theory is a branch of mathematics that deals with the analysis of strategies for dealing with competitive situations where the outcome of a participant's choice of action depends critically on the actions of other participants.
Game Theory: