Design and Analysis of Algorithms - Properties of Asymptotic Notations || GATECSE || DAA

properties of asymptotic notations || asymptotic notation properties || properties of big o notation || properties of big omega notation || properties of big oh notation || properties of theta notation || properties of notation || properties of asymptotic functions || properties of asymptotic notation in daa || asymptotic notation properties proof || properties of asymptotic notations with proofs || big o notation properties || big omega notation properties || theta notation properties Asymptotic notations are mathematical concepts used to measure the growth or decay of a function as the argument, denoted by 'n', approaches infinity. Common notations include Big-O, little-O, omega, and Theta, which are used in computer science and mathematical analysis to describe algorithm efficiency and function behavior. Contact Details (You can follow me at) Instagram: https://www.instagram.com/thegatehub/ LinkedIn: https://www.linkedin.com/in/thegatehub Twitter: https://twitter.com/THEGATEHUB ................................................................................................................... Email: [email protected] Website: https://thegatehub.com/ ................................................................................................................... 📚 Subject Wise Playlist 📚 ▶️Data Structures: http://tinyurl.com/bwptf6f7 ▶️Theory of Computation: http://tinyurl.com/5bhtzhtd ▶️Compiler Design: http://tinyurl.com/2p9wtykf ▶️Design and Analysis of Algorithms: http://tinyurl.com/ywk8uuzc ▶️Graph Theory: http://tinyurl.com/3e8mynaw ▶️Discrete Mathematics: http://tinyurl.com/y82r977y ▶️C Programming:http://tinyurl.com/2556mrmm Properties of Asymptotic Notations: Reflexivity: If f(n) is given then f(n) = O(f(n)) f(n) = Ω(f(n)) f(n) = Θ(f(n)) Symmetry: f(n) = Θ(g(n)) if and only if g(n) = Θ(f(n)) Transistivity: f(n) = O(g(n)) and g(n) = O(h(n)) ⇒ f(n) = O(h(n)) f(n) = Θ(g(n)) and g(n) = Θ(h(n)) ⇒ f(n) = Θ(h(n)) f(n) = Ω(g(n)) and g(n) = Ω(h(n)) ⇒ f(n) = Ω(h(n)) f(n) = o(g(n)) and g(n) = o(h(n)) ⇒ f(n) = o(h(n)) f(n) = ω(g(n)) and g(n) = ω(h(n)) ⇒ f(n) = ω(h(n))