The Real Analysis and Its Role with Artificial Intelligence in Future

Abstract

Merging real analysis with artificial intelligence is a vital matter for the future of technology because it provides accurate mathematical foundations that enhance the efficiency and accuracy of smart algorithms, and enables better modification and analysis of complex systems, and it is important to achieve technical progress in multiple areas. Reasons for the important integration. In artificial intelligence (AI), especially in machine learning we Know mathematical tools are linear algebra, statistics, calculus rather than real analysis. These areas provide the foundation for models and algorithm which is process data, AI and ML use linear equations, vectors and matrices to transformation and analyze data to arrive to estimated solutions. Linear Algebra is a key tool in neural networks. Calculus, probability and real analysis are key tools for optimization and dealing with imperfect data inputs in artificial intelligence and machine learning. However, the real analysis plays a significant role in advancing AI in a deeper and more formal sense.