### 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? A 10 Minute Introduction

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? A 5 Minute Introduction

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? A 5 Minute Introduction

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? A 5 Minute Introduction

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 is a Real Number? A 5 Minute Introduction

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

### What is Integration By Parts? A 5 Minute Introduction

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? A 5 Minute Introduction

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…

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

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…

### What is Lie algebra? A 5 Minute Introduction

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? A 5 Minute Introduction

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…

### What Is a Tensor? The mathematical point of view.

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

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

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…

### What Proofs are in Mathematics and Why Bother?

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

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…