Algebra beginning with I

Algebraic Terms
Click one of the letters above to go to the page of all terms beginning with that letter.
Inequality

A statement that relates one expression to another expression in one of the following:

  • is less than
  • is less than or equal
  • is greater than
  • is greater than or equal

< is read as "is less than,"
> is read as "is greater than,"
≤ is read as "is less than or equal", and
≥ is read as "is greater than or equal to"

1 is less than 5
15 is greater than 3
6 < d
11 > c
b > 5
a + 3 < 5
2z ≤ 4
3y +12 ≥ 11
Infinite Set

A set that has an unlimited number of members.

Natural Numbers, { 1, 2, 3, 4, 5, ... }
Whole Numbers, { 0, 1, 2, 3, 4, 5, ... }
Integers, { ... -2, -1, 0, 1, 2, ... }
Even Numbers, { 2, 4 , 6, 8, 10, ...}
infinity

An abstract concept describing something without limit, without end. Infinity is the largest value possible. The symbol for infinity is .

As a side note, in set theory, there are differing levels of the infinite (large beyond ???). We generally talk about infinity, but, there are different sizes of the infinite referred to as:

  • Aleph-0 (ℵ0)
  • Aleph-1 (ℵ1)
  • Aleph-2 (ℵ2).
  • (ℵ3,ℵ4, ... )

refers to the largest of all infinities

Samples:

  • Natural Numbers is a set of cardinality (size)
    Aleph-0 (ℵ0)
  • Real Numbers is a set of cardinality (size)
    Aleph-1 (ℵ1)
  • The set of all real curves is a set of cardinality (size)
    Aleph-2 (ℵ2)
Irrational Numbers

A real number that cannot be written as a simple fraction.

The following are links to samples of irrational numbers to thousands of decimal places ...
π = 3.14159 ... (Pi)
√2 = 1.4142 ... (square root of 2)
e = 2.7182 ... (Euler's number)
φ = 1.618 ... (the golden number)