Question

$1/0 = ♾ ({infinite})\ \textless \ br /\ \textgreater$
prove it ​

Answer 1

Firstly

1/0 ≠ ∞

it's just half truth!

Easy proof -––»

what is division?

well that's not topic so I won't define it!

a/b =c

a÷b=c

here we call a as dividend

b as divisor

c as quotient

so,

multiplying both sides by divisor {b}

a=cb

let's put values!

I'll prove it generally cause why do special when u can go for general {relativity☺}

taking :----»

a=a≠0

b=0 {as per question}

c= ?

a=0c

a=0

this leads to contradiction so it's undefined.. other way of looking.. there exists no no. real nor imaginary {hoping you don't know bout them but it doesn't matter} which when multiplied with 0 gives any other no. then itself zero {zero's the gangsta!!}

this way you can prove x/0= N.D {not defined} except for when x=0 {as per I know}

OTHER METHOD

––––––––––––»LIMITS«–––––––––––

It's topic of class 11 {NOT NECESSARILY TO BE STUDIED IN CLASS 11} so I'll explain briefly

we have to find x/0

so let's find {take no. near to zero}

x/0.001 =1000x

x/0.000001 =1000000x

x/0.0000000001 = 10000000000x

heya where's this going

–––» it's getting bigger and APPROACHING ∞

WHAT IF WE TOOK IT FROM THE NEGATIVE SIDE? ¿

IT'LL APPROACH -∞

as we get close to zero the different side give too different results...

AND THERE'S NO CHANCE THAT ∞ = -∞

SO ITS NOT DEFINED

HOPE IT HELPS