Mathematics FAQs

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

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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…
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 Bundles Explained: Definition, Examples & Visualization

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A fibre bundle is a mathematical structure consisting of a total space that looks locally like a simple product of two spaces but may have a different…
What are real numbers

Real Numbers Explained: Definition, Axioms & Properties

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Real numbers are the complete set of values on the continuous number line, denoted ℝ, and they include both rational numbers (fractions and repeating…
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? Equations, Focus, and Real Uses

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A parabola is a U-shaped curve where every point is equidistant from a fixed point called the focus and a fixed line called the directrix. Its standard…
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…
Lie Algebra Intro

Lie Algebras Explained: Commutators, SU(2), SO(3), Euc(n)

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A Lie algebra is the vector space of infinitesimal generators attached to a Lie group at its identity element, equipped with a bilinear antisymmetric commutator…
What is a Tangent Line

Tangent Line Equations: Circles, Curves & Surfaces Explained

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A tangent line or tangent hyperplane to a curve or surface at a given point shares the same gradient, or first-order linear approximation, as that curve…
whatisatensor

Tensors Explained: Scalars, Vectors, Matrices & Math

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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 = 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...…
proofs

Proofs in Mathematics: Methods, Examples, and How to Write Them

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A mathematical proof is a logical argument, built only from definitions, axioms, and previously established results, that shows a statement is true in…

The Concept of Zero: History, Rules, and Why 0/0 Fails

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Zero is neither positive nor negative, is defined as the additive identity so that x + 0 = x for every number x, and produces 0 when multiplied by any…