Mathematics Dictionary of Mathematics Definitions

A "baker's dozen" is 13 (A dozen is 12). In the past a baker could be fined for selling items below weight, so they added one extra "to be sure".

When both sides have the same quantity or mass.
Here "x" is balanced by 4 "1"s, so x must be 4

Banks look after peoples money, give loans and have other financial services. They must be government approved, and must follow special rules set by the government. Banks exist to make a profit for their owners.

When a person can't pay their debts they can be legally declared bankrupt.
A bankrupt person loses everything except some basic things they own, but all the debt will go away. They receive a bad credit record and may not be able to borrow money again for years.
A bankrupt company gets protection from people it owes money to (so they cannot destroy all of the physical capital and goodwill by breaking it apart and moving it away). This gives more time for the business to work out a good solution.

A graph drawn using rectangular bars to show how large each value is.
The bars can be horizontal or vertical.

The surface a solid object stands on, or the bottom line of a shape such as a triangle or rectangle. But the top is also called a base when it is parallel to the bottom!

Definition 1: The number that gets multiplied when using an exponent.
Examples:
1. in 8², 8 is the base, and the result is 8 × 8 = 64
2. in 5³, 5 is the base, and the result is 5 × 5 × 5 = 125

Definition 2: How many digits in a number system.
The decimal number system we use every day has 10 digits {0,1,2,3,4,5,6,7,8,9} and so it is Base 10.
A binary digit can only be 0 or 1, so is Base 2.
A hexadecimal digit can be {0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F}, so is Base 16.

Another name for the decimal number system that we use every day.

A thousand millions.
1,000 x 1,000,000 = 1,000,000,000
Which is a 1 followed by 9 zeros
Using scientific notation: 1 × 109
(In many non-English speaking countries it means a million million, which is a 1 followed by 12 zeros, or 1 × 1012)
Below is a cube made of a million smaller cubes. If each of the small cubes is worth a thousand dollars, then the whole cube is worth a billion dollars.

Binary Numbers use only the digits 0 and 1.

Examples:
• 0 in Binary equals 0 in the Decimal Number System,
• 1 in Binary equals 1 in the Decimal Number System,
• 10 in Binary equals 2 in the Decimal Number System,
• 11 in Binary equals 3 in the Decimal Number System,
• 100 in Binary equals 4 in the Decimal Number System,
• etc.


Also called Base 2

Binary Numbers use only the digits 0 and 1.
Examples: • 0 in Binary equals 0 in the Decimal Number System, • 1 in Binary equals 1 in the Decimal Number System, • 10 in Binary equals 2 in the Decimal Number System, • 11 in Binary equals 3 in the Decimal Number System, • 100 in Binary equals 4 in the Decimal Number System, • etc.
Also called Base 2

An operation that needs two inputs.
A simple example is the addition operation "+":
In 2 + 3 = 5 the operation is "+", which takes two values (2 and 3) and gives the result 5
Subtraction, multiplication and division are also binary operations, and there are many more.
The two inputs are called "operands".
Also, a binary operation should take and return things of the same type! In other words, the operands and the result must belong to the same Set.
An operation that has only one input is called a "unary operation".
Example: the square root function is a unary operation: √(16) = 4 has just one input "16" to produce an output of 4

A polynomial with two terms.
Example: 3x² + 2

To divide into two equal parts.
We can bisect line segments, angles, and more.
The dividing line is called the "bisector"

The line that divides something into two equal parts.
You can bisect line segments, angles, and more.

A single binary digit: 0 or 1
Example: 110100 has 6 bits.
Symbol is b
Example: 1Mb means 1 million bits

A line or border around the outside of a shape. It defines the space or area.

Either of these two:
Lower bound: a value that is less than or equal to every element of a set of data.
Upper bound: a value that is greater than or equal to every element of a set of data.
Example: in {3,5,11,20,22} 3 is a lower bound, and 22 is an upper bound
But be careful! 2 is also a lower bound (it is less than any element of that set), in fact any value 3 or less is a lower bound.
Likewise any value 22 or above is also an upper bound, such as 50 or 1000.
Example: how tall is a human? We may not know the exact shortest human, but we can say that 0 is a lower bound (can't be less than zero in height, right?)

A rectangular shape (in 2 dimensions) Or a "cuboid" (in 3 dimensions)

Another name for Width.
Example: the breadth of the door is 80 cm.

An estimate of income and spending for some period of time.
Example: Sam has a weekly budget to make sure there is enough money at the end of the week for a night out.
Example: HappyPup Ltd has just finished their Yearly Budget and has set aside $20,000 for the local animal shelter.

8 binary digits
A single binary digit (called a "bit") can only be 0 or 1
Example: 1 is a bit
Example: 10110110 is a byte
A bit can have only 2 different values: 0 or 1
A byte can have 2×2×2×2×2×2×2×2 = 256 different values

Symbol is B (and b means bit)
Example: 1MB means 1 million bytes (or 8 million bits)