ch 2: mathematical language and symbols Flashcards
is a complex system of words and symbols, either spoken or written, used by a particular community as a means of communication.
Language
A system used by mathematicians to communicate mathematical ideas among themselves.
Language of Mathematics
Every language has its vocabulary (the words) and its rules for combing these words into complete thoughts (the sentences).
Language of Mathematics
express formulas or to represent a constant.
Symbols
facts, names, notation, or usage which is generally agreed upon by mathematicians.
Conventional
means standard/aplicable to all
Conventional
to make the expression well-formed to make characters and symbols clear and does not violate the rules.
Syntax
it also when there is no error and you get the correct answer
Syntax
it is also when the design and measurement are clear and understadable
Syntax
Math is comprised of primarily two things, which are?
numbers and symbols.
it occurs when there is something wrong or when the input cannot be read/interpreted (by the calculator/user?)
Syntax error
can symbols be letters or not?
symbols cannot be letters
Characteristics of the Language of Mathematics
(enumerate)
- Precise
- Concise
- Powerful
able to make very fine distinctions.
Precise
this word can also mean(?) almost/approximately equal to
Precise
able to say things briefly.
Concise
able to express complex thoughts with relative ease.
Powerful
are combination of finite symbols that follows mathematical rules
Mathematical Expression
are correct arrangement that represents mathematical objects
Mathematical Expression
these does not have a complete thought
Mathematical Expression
are neither true nor false
Mathematical Expression
most common expressions
(enumerate)
- Numbers and Variables
- Sets
- Functions
- Relations
Analogue of an English sentence
Mathematical Sentences
Correct arrangement that represents a complete thought
Mathematical Sentences
Use equality symbols to compare two expressions
Mathematical Sentences
Always true or false, sometimes true and sometimes false
Mathematical Sentences
Most common sentences
(enumerate)
- Mathematical formula
- Mathematical theories
- Mathematical postulates and corollaries
- Equations and Inequalities
in Performing Operations on Mathematical Expression Correctly, you use?
G-E-M/D-A/S
a mnemonic used to remember the order of operations in math problems.
G-E-M/D-A/S
it does not have an equal sign
Mathematical Expression
explain each component of G-E-M/D-A/S
G - simplify everything inside the GROUPING SYMBOL.
E - simplify every EXPONENTIAL NUMBERS in the numerical expression.
M/D - Multiply or Divide whichever comes first, FROM LEFT TO RIGHT.
A/S - FROM LEFT TO RIGHT, add or subtract whichever comes first.
has an equal sign
Mathematical Senetnces
enumerate all the symbols
- ”+” add
- ”-“ subtract
- “×” multiply
- “÷” divide
- ”/” divide
- ”( )” grouping symbols (aka. parenthesis)
- ”[ ]” grouping symbols (aka. square brackets)
- ”{ }” set symbols (aka. flowery brackets)
- “π” pi
- “∞” infinity
- ”=” equals
- “≈” approximately equal to
- “≠” not equal to
- ”<” , “≤” less than, less than or equal to
- ”>” , “≥” greater than, greater than or equal to
- “√ “ square root (“radical”)
- “°” degrees
- “∴” therefore
it is also known as “repeated addition” or “skip counting”
multiplication
asside from the multiplication symbol, we also use these to apply the operation of multiplication
() and []
more complicated equations/expressions use this
[] or grouping symbol
used when the content share common properties/characteristics or when listing them
{} or set symbol
what do you call the contents inside a {}
elements
without this, the thought is incomplete
=
ususally used when we round off the value
≈ or approximately equal to
used indicated how many times a number is multiplied to itself
√
used to express angles or temperatures
° or degrees
used when you make a judgement, conclusion, or interpretation based on the given requirements
∴ or therefore
