many people say that the 0^(0 ) is an uninfinity ones of them say that 0^0 is infinity and equal to 1! what do you think wich ones of them say right?


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Question Number 192604 by sciencestudentW last updated on 22/May/23

$m a n y p e o p l e s a y t h a t t h e 0^{0} i s a n u n i n f i n i t y$ $o n e s o f t h e m s a y t h a t 0^{0} i s i n f i n i t y a n d e q u a l t o 1!$ $w h a t d o y o u t h i n k w i c h o n e s o f t h e m$ $s a y r i g h t ?$
Commented by Frix last updated on 22/May/23
$There′s no right or wrong. It depends on how you define it. 0^n =0∀n∈N\{0} ⇒ we can define 0^0 =0 r^0 =1∀r∈R\{0} ⇒ we can define 0^0 =1 ... lim_(x→0) (x/(sin x)) =1 lim_(x→0) ((sin x)/x) =1 lim_(x→0) (x^2 /(sin x)) =0 lim_(x→0) ((sin x)/x^2 ) =undefined ...$
${There}^{'} s no right or wrong . It depends on$ $how you define it .$ $0^{n} = 0 \forall n \in N ∖ {0} \Rightarrow we can define 0^{0} = 0$ $r^{0} = 1 \forall r \in R ∖ {0} \Rightarrow we can define 0^{0} = 1$ $. . .$ $\lim_{x \to 0} \frac{x}{\sin x} = 1 \lim_{x \to 0} \frac{\sin x}{x} = 1$ $\lim_{x \to 0} \frac{x^{2}}{\sin x} = 0 \lim_{x \to 0} \frac{\sin x}{x^{2}} = undefined$ $. . .$
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