I am a secondary student lost in the world of maths, puzzles, and am always trying to poke my nose in some sort of math. ©

जनुना तलावं ©

I am the Owner of Breakaway Transportation with a background in programming in Java, C++, and VBA. ©

I`d just like to interject for a moment. What you`re referring to as calculus, is in fact, real analysis, or as I`ve recently taken to calling it, $left( mathbf R,, +,, times,, leqslant,, left cdot right ,, tau ,=, left{ A ,subset, mathbf R mid forall x,in, A,, exists varepsilon ,>, 0,, left] x ,-, varepsilon,, x ,+, varepsilonright[ ,subset, A right},, bigcap_{begin{array}{c} A ,sigma text{-algebra of}, mathbf R tau ,subset, A end{array}} A,, ell right)$-analysis. Calculus is not a branch of mathematics unto itself, but rather another application of a fully functioning analysis made useful by topology, measure theory and vital $mathbf R$-related properties comprising a full number field as defined by pure mathematics. Many mathematics students and professors use applications of real analysis every day, without realizing it. Through a peculiar turn of events, the application of real analysis which is widely used today is often called Calculus, and many of its users are not aware that it is merely a part of real analysis, developed by the Nicolas Bourbaki group. There really is a calculus, and these people are using it, but it is just a part of the field they use. Calculus is the computation process: the set of rules and formulae that allow the mathematical mind to derive numerical formulae from other numerical formulae. The computation process is an essential part of a branch of mathematics, but useless by itself; it can only function in the context of a complete number field. Calculus is normally used in combination with the real number field, its topology and its measured space: the whole system is basically real numbers with analytical methods and properties added, or real analysis. All the so-called calculus problems are really problems of real analysis. ©