Introduction

Notation is a system of symbols, marks, or characters used to represent information, ideas, or elements in a structured and standardized way. Notation systems are crucial in various fields, including mathematics, music, science, and language, as they allow complex ideas to be communicated efficiently and accurately. Whether through letters, numbers, symbols, or other characters, notation serves as a universal language within specific disciplines, enabling people to share and understand information with clarity.

Music Notation

♩ ♪ ♫ ♬ 𝄞 𝄢

Algebraic Notation

• \( x + y = z \)
• \( a^2 + b^2 = c^2 \)
• \( 3x - 7 = 2 \)

Set Notation

• \( \{1, 2, 3\} \)
• \( \{x \mid x > 0\} \)

Empty set

• \( \emptyset \)

Function Notation

• \( f(x) = x^2 \)
• \( g(x) = 2x + 3 \)
• \( h(a, b) = a + b \)

Summation Notation (Sigma Notation)

• \( \sum_{i=1}^{n} i \)
• \( \sum_{k=0}^{\infty} \frac{1}{2^k} \)
• \( \sum_{j=1}^{5} j^2 \)

Integral Notation

• \( \int_{0}^{1} x^2 \, dx \)
• \( \int f(x) \, dx \)
• \( \int_{a}^{b} (2x + 3) \, dx \)

Matrix Notation

• \( A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \)
• \( B = \begin{pmatrix} a & b \\ c & d \end{pmatrix} \)
• \( C = \begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix} \) (Identity Matrix)

Alphabets as Notation

• Latin Alphabet A, B, C, D
• Greek Alphabet α, β, γ, δ
• Cyrillic А, Б, В, Г