## Mandy

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Counting Numbers:

### {1, 2, 3, 4, 5, 6, ...}

BY THE WAY, "..." notates continuation going up infinitely.

The set of **Natural Numbers** \( \mathbb{N}\ \ \) = {0, 1, 2 3, 4, 5, 6...}.

The set of **Integers**, \( \mathbb{Z}\ \ \) = {..., -3, -2, -1, 0, 1, 2, 3}.

The set of **Rational numbers**, \( \mathbb{Q}\ \ \) is the set of ratios of integers.

That is, every \(q \in \mathbb{Q}\ \)

is of the form:

\( q = \frac{n}{m} \ \)

With \( n, m \in \mathbb{Z}\ \) .

The set of **Real Numbers** \( \mathbb{R}\ \ \) is the set of limits of sequences of rational numbers.

A **set **is a collection of "elements," or "members," and each set is entirely determined by its members. If \[ x \]is a member of a set \[ U, \] we write \[ x \in U. \] In basic algebra, the elements of a set are usually numbers.

We can also designate a set by enclosing its members in braces , { }.

All equations have various parts. The variable represents the unknown. We can tell what "x" represents in this particular equation, almost by guessing. WHAT + 23 = 45?

The VARIABLE here is "x"

The CONTANT is 23, because it is "constantly" there, and we have already identified its value as 23.

Mathematically, we can obtain what "WHAT" equals, by subtracting 23 from 45.

45 - 23 = 22

Therefore, x = 22

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