Tag Archive for: limits

Epsilontic limits and continuity

Epsilontic – Limits and Continuity

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Abstract I remember that I had some difficulties moving from school mathematics to university mathematics. From what I read on PF through the years, I…
calc precalc

Beginners Guide to Precalculus, Calculus and Infinitesimals

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Introduction I am convinced students learn Calculus far too late.   In my view, there has never been a good reason for this.In the US, they go through…
Infinitesimals

What Are Infinitesimals – Simple Version

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Introduction When I learned calculus, the intuitive idea of infinitesimal was used. These are real numbers so small that, for all practical purposes (say…
Infinitesimals

What Are Infinitesimals – Advanced Version

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Introduction When I learned calculus, the intuitive idea of infinitesimal was used. These are real numbers so small that, for all practical purposes (say…
Integral Representations of Some Special Functions

The Orin Fractional Calculus

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Introduction This bit is what new thing you can learn reading this:) As for original content, I only have hope that the method of using the sets $$C_N^n:…
Limit of a Function

What Is a Limit of a Function? Definition, Laws & Examples

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A limit describes the value a function or sequence approaches as its input gets arbitrarily close to a specific point, without requiring the function to…
999equals1

Why 1 = 0.999…: Four Simple Proofs Explained

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Yes, 1 and 0.999... are exactly the same real number, not merely two numbers that happen to be extremely close. This surprises many people because 0.999...…
infinity_faq

Infinity in Mathematics: What It Really Means, Explained

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Infinity is not a real number but a set of distinct mathematical tools, including the extended real line, the projective real line, the Riemann sphere,…
999

Is 1 Equal to 0.999…? Rigorous Proof Explained

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101 Comments
Yes, 1 equals 0.999... exactly, not approximately. This is a proven mathematical fact once the notation 0.999... and the concept of an infinite sum are…