Monotonia, in mathematics, refers to the property of a function that either never decreases or never increases as its independent variable increases. More formally, a function is said to be monotonic if it is either entirely non-increasing or entirely non-decreasing.
There are different types of monotonicity:
Monotonically Increasing (Non-decreasing): A function f(x) is monotonically increasing if for any x₁ and x₂ such that x₁ ≤ x₂, we have f(x₁) ≤ f(x₂). This can also be described as increasing functions.
Strictly Increasing: A function f(x) is strictly increasing if for any x₁ and x₂ such that x₁ < x₂, we have f(x₁) < f(x₂).
Monotonically Decreasing (Non-increasing): A function f(x) is monotonically decreasing if for any x₁ and x₂ such that x₁ ≤ x₂, we have f(x₁) ≥ f(x₂). This can also be described as decreasing functions.
Strictly Decreasing: A function f(x) is strictly decreasing if for any x₁ and x₂ such that x₁ < x₂, we have f(x₁) > f(x₂).
Monotonic functions are important in various areas of mathematics, including calculus, real analysis, and optimization. They have useful properties that simplify analysis and can be found in problems related to inequalities and sequences.
Ne Demek sitesindeki bilgiler kullanıcılar vasıtasıyla veya otomatik oluşturulmuştur. Buradaki bilgilerin doğru olduğu garanti edilmez. Düzeltilmesi gereken bilgi olduğunu düşünüyorsanız bizimle iletişime geçiniz. Her türlü görüş, destek ve önerileriniz için iletisim@nedemek.page