1. The problem is to understand the difference between $\omega$ and $\Omega$ in mathematics and science. 2. $\omega$ (lowercase omega) is often used to represent angular frequency in physics, or a variable in mathematics, especially in trigonometry and complex numbers. 3. $\Omega$ (uppercase Omega) is commonly used to denote ohms (unit of electrical resistance), the sample space in probability, or the asymptotic upper bound in computer science. 4. Important rule: Greek letters have different meanings depending on context, and case (uppercase vs lowercase) matters. 5. Summary: $\omega$ is lowercase omega, often angular frequency; $\Omega$ is uppercase Omega, often a unit or set notation.