Q40. - Algebra 2

Question

Use the following information.

The Greek mathematician Pythagoras believed that all things could be described by numbers. By “number” he meant positive integers.

To what set of numbers was Pythagoras referring when he spoke of “numbers?” 

Step-by-Step Solution

Answer

Pythagoras referring to Natural Numbers when he spoke of “numbers”.

Step 1 - Define different sets

• The set $\left\{1,2,3,4,5,...\right\}$ is called the set of natural number. 
• The set $\left\{0,1,2,3,4,5,...\right\}$ is called the set of whole number. 
• The set $\left\{-3,-2,-1,0,1,2,3,...\right\}$ is called the set of integer number.
• The set of rational number has numbers in the ratio form $\frac{m}{n}$, where $m$ and n are integers and n is non-zero. The decimal form of a rational number is either a terminating or repeating decimal.
• A real number that is not rational is irrational. The decimal form of an irrational number is neither terminating nor rational.
• Combine sets of rational and irrational number is real number.

Step 2 - Relationship between different sets

Following vein diagram shows relationship between different sets

Where, the symbols denote 

N- Natural number

W- Whole number

Z- Integers

Q- Rational number

I- Irrational number

R- Real numbers

Step 3 - Define positive integers

Using image, all natural numbers are whole numbers and all whole numbers are integers. So, meaning of positive integers is natural number.