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In mathematics, non-classical analysis is any system of analysis, other than classical real analysis, and complex, vector, tensor, etc., analysis based upon it.

Such systems include:

Non-standard analysis and the calculus it involves, non-standard calculus, are considered part of classical mathematics (i.e. The concept of "hyperreal number" it uses, can be constructed in the framework of Zermelo–Fraenkel set theory).

Non-Newtonian calculus is also a part of classical mathematics.
References

"Paul Taylor's site". Paultaylor.eu. Retrieved 2013-09-23.

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