could you please ellaborate about them both?Originally posted by rutwig
Now, you want the Robinson point of view or the internal set theory of Nelson?
Originally posted by loop quantum gravity
could you please ellaborate about them both?
Nonstandard analysis is a branch of mathematics that extends the traditional real number system to include infinitesimal and infinite numbers. It was first developed by Abraham Robinson in the 1960s as an alternative to the more classical approach to real analysis.
Nonstandard analysis has applications in various fields of mathematics, including calculus, differential equations, and functional analysis. It has also been used in physics and economics to model continuous processes and systems.
Traditional analysis is based on the concept of limits, where infinitesimal and infinite quantities are not allowed. Nonstandard analysis, on the other hand, allows for the use of infinitesimals and infinities as part of the number system.
Nonstandard analysis has gained acceptance in the mathematical community, although it is still considered a relatively new and developing field. It has been used to prove results that were previously unattainable using traditional analysis, and has sparked new research and developments in various areas of mathematics.
Some mathematicians argue that nonstandard analysis is not rigorous enough and relies too heavily on intuition. It also requires a thorough understanding of the theory and can be difficult to apply in certain situations. However, many believe that the benefits of using nonstandard analysis outweigh these drawbacks.