Arithmetic

Arithmetic is a branch of mathematics that studies numbers, their properties, and the basic operations performed on them.

The Basic Concept of Arithmetic

Basic Arithmetic Operations

1. Addition (+) — combining two numbers into a single value.
   • Example: 7 + 5 = 12.
2. Subtraction (-) — finding the difference between numbers.
   • Example: 10 - 4 = 6.
3. Multiplication (× or *) — repeated addition.
   • Example: 3 × 4 = 12.
4. Division (÷ or /) — dividing a number into equal parts.
   • Example: 12 / 3 = 4.

Order of Operations

When evaluating expressions, the following order of precedence is used:

1. Operations inside parentheses.
2. Multiplication and division.
3. Addition and subtraction.

Example:

2 + 3 × 4 = 2 + 12 = 14

Properties of Operations

• Commutative property of addition: a + b = b + a.
• Commutative property of multiplication: a × b = b × a.
• Associative property of addition: (a + b) + c = a + (b + c).
• Distributive property: a × (b + c) = a × b + a × c.

Why Arithmetic Is Needed

Arithmetic is used every day when calculating time, money, purchases, distances, and solving other practical problems.

Philosophy of Arithmetic

1. In arithmetic, a number pertains to objects of reality that belong to the same category. You cannot add two apples and two liters of water.
2. In reality, there are no twos, threes, or fives. A number appears when consciousness describes an observation and
   compresses a multiplicity of objects into a single quantitative expression. That is, we see: a log, a log, a log — but describe
   this as three logs.
3. In other words, consciousness says, “this is the same, this is the same, this is the same,” and then groups these things together and denotes them
   with a number.
4. A number is the quantity of repetitions of the same thing. More precisely, it is the quantity of things that consciousness has categorized as the
   same. Strictly speaking, nothing in reality is absolutely identical to anything else, so treating anything as a repetition is exclusively
   a way for consciousness to simplify reality.