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Mathematical Language and Symbol : Variables

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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

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

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

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

statements

all positive numbers are greater than zero

are greater than zero

so unconditional statement says if one

thing is true

then some other thing also has to be true

true

for example if 378 is divisible by 18

and i'm not saying this is divisible so

if i think this is true

lyon then three seven eight is divisible

by six so

existential statement

says that there is at least one thing

for which

the property is true for example

while for the universal conditional

statement so a statement that is bought

universal and conditional so this will

be a combination of universal and

conditional statement for all animals a if

a is a dog then a is a mammal so they

can be written in ways that make them

appear to be purely universal or purely

conditional so statement

so if a is a dog

then a is a mammal so purely condition aliba

aliba so

so don

don

or if an animal is a dog then the animal

so for example

if a real number is not zero then each

square is anna

yeah

you know

onion number one yes

yes

it's a facility

for all non-zero

real number is x

and that's a good

yeah you're right that is x squared is positive

positive

okay if x blank then blank

if x is a nonzero real number then

then

so for the universal existential

statements so a statement that is

universal because its first part says

that a certain property is true for all

objects of a given type and it is ex

existential because its second part

asserts the existence of something

for example every every real number has

an additive inverse

all real numbers have an added

let's have an additive real numbers for

all real numbers or there is an additive inverse

inverse

for all real numbers are there is a real

number such as on s such as s is an additive

additive inverse

inverse

so you know adding

okay next so

for this statement that is existential

because its first part asserts

that a certain object is exists and is

universal because its second part says

that the object satisfy a certain

property for all things of a certain kind

kind

for example we have there is a positive

integer that is less than or equal to

i hope

may join us on the new acting lecture

for the variables so

not we're going to discuss for another

topic under the

mathematical language

so i hope nintendo ciao

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YouTube Transcript:Mathematical Language and Symbol : Variables