Math FAQs

Here contains the collection of Insight math FAQs. These are commonly asked questions and misconceptions that inside are corrected and answered. Disciplines from algebra to advanced calculus with the student in mind. Learn something new today!

infinity

Why Division by Zero is a Bad Idea

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A division by zero is primarily an algebraic question. The reasoning therefore follows the indirect pattern of most algebraic proofs: What if it was allowed? Then…
How to Find Potential Functions

How to Find Potential Functions? A 10 Minute Introduction

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Definition/Summary Given a vector field ##\vec F(x,y,z)## that has a potential function, how do you find it? Equations $$\nabla \phi(x,y,z) = \vec F(x,y,z)$$…
What is a linear equation

What is a Linear Equation? A 5 Minute Introduction

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Definition/Summary A first-order polynomial equation in one variable, its general form is [itex]Mx+B=0[/itex] where x is the variable. The quantities…
What are significant figures

What are Significant Figures? A 5 Minute Introduction

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Definition/Summary Significant figures (commonly called "sig figs") are the number of figures (digits) included when rounding-off a number.For example,…
What is a fibre bundle

What is a Fibre Bundle? A 5 Minute Introduction

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Definition/Summary Intuitively speaking, a fibre bundle is space E which 'locally looks like' a product space B×F, but globally may have a different…
What are real numbers

What is a Real Number? A 5 Minute Introduction

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Definition of real numbers Real numbers are a comprehensive set of numbers that encompasses all possible values on the number line. They include both…
integration by parts

What is Integration By Parts? A 5 Minute Introduction

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Definition/Summary In this article, we shall learn a method for integrating the product of two functions. This method is derived from the 'product rule'…
What is a parabola

What is a Parabola? A 5 Minute Introduction

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What is a Parabola? A parabola is a U-shaped curve in mathematics that is defined by a specific set of points. It is a fundamental geometric shape that…
Limit of a Function

What Is a Limit of a Function? A 5 Minute Introduction

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What is a limit? In mathematics, a limit is a fundamental concept used to describe the behavior of a function or sequence as it approaches a particular…
Lie Algebra Intro

What is Lie algebra? A 5 Minute Introduction

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Definition/Summary A Lie algebra ("Lee") is a set of generators of a Lie group. It is a basis of the tangent space around a Lie group's identity element,…
What is a Tangent Line

What is a Tangent Line? A 5 Minute Introduction

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Definition/Summary The tangent to a curve in a plane at a particular point has the same Gradient as the curve has at that point.More generally, the…
whatisatensor

What Is a Tensor? The mathematical point of view.

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Key pointsThe author begins by questioning the nature of numbers and their deeper significance. Numbers can represent various mathematical constructs,…
999equals1

Why Do People Say That 1 And .999 Are Equal?

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Why do people say 1 and 0.999... are equal? Aren't they two different numbers?No, they really are the same number, though this is often very counterintuitive…
proofs

What Proofs are in Mathematics and Why Bother?

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This FAQ is about proofs. Proofs are central to mathematics, and writing proofs is for many people a skill that is hard to master. There are actually two…

The History and Concept of the Number 0

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The goal of this FAQ is to clear up the concept of 0 and specifically the operations that are allowed with 0.The best way to start this FAQ is to look…