2^(2^n)=O(2^n). Is it true or false?

Thanks in advance

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Do you think it's true or false? What have you trieed to prove or disprove it? What's the definition of big-Oh - how would `2^(2^n)` need to relate to `2^n` for `2^(2^n)` to be in `O(2^n)`?

## All 3 Replies

Do you think it's true or false? What have you trieed to prove or disprove it? What's the definition of big-Oh - how would `2^(2^n)` need to relate to `2^n` for `2^(2^n)` to be in `O(2^n)`?

Greetings,

First of all, let g and f be two given functions :

f(x)belongs to O(g(x)) iff: there is some c of R+ such that:

``````                               f(x)<= c*(g(x)) . . .(1)
``````

Thus, from (1) we can conclude that 2^(n)<= 2^(2^n) where c=1,

Then, 2^(n) belongs to O(2^(2^n)).

Interesting how can this algoritm being used in computer science

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