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 a Potential Function of a Vector Field

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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

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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

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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

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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 & Axioms — Explained

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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

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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

Parabola: Definition, Equations & Applications — 5-Min Guide

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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

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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

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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 to a Curve: Definition, Equations & Examples

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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 at that point.More generally, the…
whatisatensor

What Is a Tensor? The mathematical point of view.

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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

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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

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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!

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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…