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 Impossible: 10 Mathematical Reasons

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

How to Find a Potential Function of a Vector Field

/
0 Comments
Definition and summary Given a vector field ##\vec F(x,y,z)## that has a potential function, how do you find it? Conditions and equations $$\nabla \phi(x,y,z)…
What is a linear equation

First-Order Linear Equation: Definition & Solutions

/
0 Comments
Definition / Summary This article summarizes the first-order (linear) polynomial equation in one variable, its solution, and natural extensions to matrices…
What are significant figures

Significant Figures: Rounding Rules & Examples for Science

/
0 Comments
Definition / Summary Significant figures (commonly called "sig figs") are the digits in a number that are considered when rounding a value to reflect…
What is a fibre bundle

Fibre Bundle: Definition, Examples & Intuitive Guide

/
3 Comments
Definition / Summary Fibre bundle — intuitively, a fibre bundle is a space E that locally looks like a product B × F but may have a different global…
What are real numbers

Real Numbers: Definition, Properties & Completeness

/
0 Comments
Definition of real numbers Real numbers are the set of all values that can appear on the continuous number line. They include rational numbers (fractions…
integration by parts

What is Integration By Parts? A 5 Minute Introduction

/
0 Comments
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

Parabola Explained: Properties, Equations & Practical Uses

/
0 Comments
What is a Parabola? A parabola is a U-shaped curve that appears frequently in mathematics, physics and engineering. It is a conic section defined by a…
Limit of a Function

Limits of Functions for Calculus: Definition & Examples

/
0 Comments
What is a limit? In mathematics, a limit describes the behavior of a function or sequence as its input approaches a particular value. Limits are a cornerstone…
Lie Algebra Intro

Lie Algebra Basics: Definitions, Equations & Examples

/
0 Comments
Definition / Summary A Lie algebra (pronounced "Lee") is the tangent-space algebra of a Lie group at its identity element. Concretely, it is a vector…
What is a Tangent Line

Tangent Line and Hyperplane: Definitions & Circle Example

/
0 Comments
Definition / Summary Informal idea The tangent to a curve in a plane at a particular point has the same gradient as the curve at that point. Generalization More…
whatisatensor

Tensors Explained: Scalars, Vectors, Matrices & Math

/
58 Comments
Introduction Let me start with a counter-question. What is a number? Before you laugh, there is more to this question than one might think. A number can…
999equals1

Why 1 Equals 0.999… — Explanations & Rigorous Proofs

/
111 Comments
Why do people say 1 and 0.999... are equal? Aren't they two different numbers? No — 1 and 0.999... really are the same number, although that can feel…
proofs

Mathematical Proofs: How to Understand and Write Them

/
28 Comments
Introduction This FAQ is about proofs. Proofs are central to mathematics, and writing proofs is a skill many people find hard to master. There are two…

Understanding Zero: History, Division, Exponents, 0!

/
7 Comments
The goal of this FAQ is to clarify the concept of 0, and specifically the operations that are allowed with it.The best way to start this FAQ is to…