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ajprincess
 2 years ago
Please help:)
Prove that if ab and ba, then \(a=\pm b\)
ajprincess
 2 years ago
Please help:) Prove that if ab and ba, then \(a=\pm b\)

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sauravshakya
 2 years ago
Best ResponseYou've already chosen the best response.4Let x=a/b then since b divides a, x is a integer other than 0 Now, Since a also divides b b/a is also integer other than 0 Here, b/a =1/(a/b) =1/x So, x can be either +1 or 1

sauravshakya
 2 years ago
Best ResponseYou've already chosen the best response.4Now, when x=1 then a/b=1 ===>a=b when x=1 then a/b=1 =====>a=b

ajprincess
 2 years ago
Best ResponseYou've already chosen the best response.0Thanx a lottt @sauravshakya.:)

jiteshmeghwal9
 2 years ago
Best ResponseYou've already chosen the best response.0@sauravshakya i couldn't understand ur statement ``` Now, Since a also divides b b/a is also integer other than 0 ```

jiteshmeghwal9
 2 years ago
Best ResponseYou've already chosen the best response.0@ajprincess can u tell me the statement in easier way ??

ajprincess
 2 years ago
Best ResponseYou've already chosen the best response.0ab is a notation that means a divides b and b/a is an integer. ba is a notation that means b divides a and a/b is an integer.

ajprincess
 2 years ago
Best ResponseYou've already chosen the best response.0ab can also be expressed in this way b/a=x, x is an integer. If x is o , b must be equal to 0. ba can also be expressed in this way a/b=y, y is an integer a/0=infinity. infinity is not an ineger that is y we give the condition that x is an integer except 0. getting it @jiteshmeghwal9?

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.0Hmm, I take it that you meant a/0 is not defined.

jiteshmeghwal9
 2 years ago
Best ResponseYou've already chosen the best response.0ya! I gt it a little but \(\frac{a}{b}\) doesn't this mean b divides a

ajprincess
 2 years ago
Best ResponseYou've already chosen the best response.0ya u can take it that way @parthkohli

ajprincess
 2 years ago
Best ResponseYou've already chosen the best response.0ab and a/b are different.

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.0\[a\ne 0, b \ne 0\]because if one of them is zero, then one of \(ab\) or \(ba\) will be false. =)

jiteshmeghwal9
 2 years ago
Best ResponseYou've already chosen the best response.0ohh ! i thought it is a/b i gt it completely, thanx :)

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.0\(ba\) is the same as \(bx = a :x\in \mathbb{Z}^{+}\)

ajprincess
 2 years ago
Best ResponseYou've already chosen the best response.0ya u are absolutely right:) @ParthKohli and welcome:) @jiteshmeghwal9

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.0Nice proof! @sauravshakya
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