This content introduces the concept of variables in mathematical language and explores different types of mathematical statements, including unconditional, existential, universal conditional, universal existential, and existential universal statements.
now we are going to discuss for the
another topic under the mathematical
language and symbols that is variables
okay so
what is variables it is represented by a letter
letter
z
y or
a n or a and b
as a symbol
example for example so we is there a
number with the
following property so doubling it and
adding three gives the same result as
so then is there a
number x
with the property that 2x
plus 3
is equal to x squared
double double
doubling it and adding 3 gives the same
result as squaring it
or is there a number of x with the
property that um
is there a number to check nothing
to illustrate the second use of the
variables considered statements no
matter what number might be chosen if it
is greater than two then square is
greater than four
don't hide a new numbering animal
okay so
introducing a variable to give a
temporary name to the number that you
might choose enables you to maintain the generality
generality
of this statement
is there a number x with the property
that 2x plus 3 is equal to x squared
so no matter what number might be chosen
if it's greater than 2 then its square
is greater than four
four
you know
no matter what number
might be chosen
if x is greater than two
then x squared is greater than four
writing a sentence using variables so
use variables to rewrite the following
sentence more formally so
so
are there numbers with the property the
sub that sum that the sum of their
squares equals so the
square of their sum
sum or
or
give any real number its square is non-negative
non-negative
checking
are there a number x and y
with the property of x squared plus y
squared is equal to quantity of x plus y
are there numbers
numbers
sentences such that x squared plus y
squared is equal to quantity of x plus y
or do there exist any numbers
x and y such that x squared plus y
squared is equal to quantity x plus y
for letter b
give any real number so r squared is none
none
negative so for any real numbers that r
r is equal r squared is greater than or
or for all real number or is r squared
is greater than or equal to zero
actually there are
so some important kinds of mathematical statements
