Why $n ≃ i$?

I mean suppose $n=1000$ and so $i= 2,4,16,32,256,65536$ is in every steps.

In the book wrote $2^2 power(k)$ is pattern for growing $i$ so $n ≃ i$ and...

Now 65536 or 256 isn't equal to 1000 or around 1000.

But why $n ≃ i$?

This chapter is about notations.

  • 1
    $\begingroup$ How does your source define this notation? It is impossible to answer your question without this knowledge. $\endgroup$ – Juho Dec 10 '19 at 15:05

The symbol $\space ≃ \space$ means "asymptotically equal to".

So when you read $ n ≃ i$, you can read it as $n$ asymptotically approaches $i$.

This means that the more $n$ increase in size, the more $i$ increase in size but $n$ never become equal to $i$.

I mean suppose $n=1000$ and so $i=2,4,16,32,256,65536$ is in every steps.

This contains an error: when the program start $i=2$. At the first cicle, $i=2^2 = 4 $. $\space$ At the second cicle, $i=4^2=16$. $\space$ At the third cicle, $i = 16^2= 256$. $\space$ At the fourth cycle, $i=256^2 = 65536$. $\space$ At the fifth cycle the program stops since $i>n$.

  • $\begingroup$ I think $i$ asymptotically approaches $n$ . because $i$ in every step is go on and $n$ is fixed?!(please see the code) $\endgroup$ – Michael Dec 10 '19 at 16:34

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