Infimum: The Greatest Lower Bound | Wiki Coffee
The infimum, denoted as inf, is a fundamental concept in mathematics that represents the greatest lower bound of a set of numbers. It is a crucial idea in…
Overview
The infimum, denoted as inf, is a fundamental concept in mathematics that represents the greatest lower bound of a set of numbers. It is a crucial idea in real analysis, topology, and other branches of mathematics. The infimum is often contrasted with the supremum, which is the least upper bound of a set. While the supremum is the smallest number that is greater than or equal to all elements in the set, the infimum is the largest number that is less than or equal to all elements in the set. For example, the infimum of the set of all positive real numbers is 0, since 0 is the greatest lower bound of this set. The concept of infimum has far-reaching implications in various fields, including calculus, optimization, and mathematical physics, with a vibe score of 8 due to its significant influence on the development of modern mathematics.
Key Facts
- Year
- 1870
- Origin
- Augustin-Louis Cauchy and Karl Weierstrass
- Category
- Mathematics
- Type
- Mathematical Concept