The Language of Mathematics

1

Bellringer

Look through the scope and sequence to see what's

being taught between the old and new curriculum.

Q: 1. Why is mathematics called “the universal language”?

2. What notation and vocabulary do I need to know?

3. How do sets of numbers relate to one another?

4. What does it mean for a set of numbers to be dense?

5. What does it mean for a set of numbers to be closed under an operation?

The Language of Mathematics

2

Consider: The Formal Definition of a Limit

Example

set

“member of” a set

empty set

subset

“such that”

excluding/”except for”

universal quantifier

existential quantifier

The Language of Mathematics

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intersection of sets union of sets

Bellringer - on desk

The Language of Mathematics

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B. Rewrite using mathematical notation:

1. “for some x such that x is not a member of the set of real numbers”

2. “y such that y is a member of the empty set”

3. “the set of positive integers, excluding –2”

4. “the set of numbers 1, 2, 3, is a subset of the complex numbers”

The Language of Mathematics

5

Bellringer - on desk

real number line

density

Are the integers dense? Explain:

closure

Under which operations are the whole numbers closed? Explain:

the line whose points are all the real numbers

a set of numbers is dense if between any 2 members you can find

a third member.

a set has closure under an operation if performance of that operation

on members of the set always produces a member of the set.

The Language of Mathematics

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finite

infinite:

The Language of Mathematics

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Convert interval notation to inequality notation or vice versa. State whether the interval is bounded or unbounded, its type, and graph the interval.

1. [-6, 3) 2. (- , -1) 3. –2 < x < 3

4. [0, 11] 5. (-4, 1) 6. 12 < x ≤ 100

II. Rewrite using mathematical notation:

1. “for all x that is not a member of the set of integers”

2. “there exists a y such that y is a member of the set of negative real numbers”

3. “the set of whole numbers, excluding 5”

4. “the set of numbers 1, 2, 3, is a subset of the positive integers”

1. The set of natural numbers is a subset of the set of whole numbers. _____

_____

3. The set of rational numbers is a subset of the set of real numbers. _____

. _____