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In set $T = \{(0+2)^{i+5}|\space i \in \mathbb{N}\}$, what is the meaning of the $(0+2)^{i+5}$?

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doesnt it take on the normal meaning? –  Jorge Fernández Aug 31 '12 at 0:09
    
what is the difference between 0+2 and just 2? –  Jorge Fernández Aug 31 '12 at 0:10
    
that is what I was wondering. but apparently 0,2 should be considered as characters that make up a string.. (why they wouldn't just use 0,1 idk) –  James Aug 31 '12 at 0:11
    
where did you see that? –  Jorge Fernández Aug 31 '12 at 0:14
    
It is from my problem set, not a text. To add some context, all the previous problems considered numbers as characters. That is, 10 is not ten but one-zero. –  James Aug 31 '12 at 0:17

2 Answers 2

up vote 3 down vote accepted

A likely possibility, given your comment, is that $(0+2)$ is to be interpreted as a regular expression, namely "either 0 or 2" and the apparent exponentiation would be read as concatenation of the elements ({0, 2}) of that set. Under this reading, the set $T$ would be (assuming $\mathbb{N}$ doesn't include zero) $\{000000, 022222,0202020200002, , \dots\}$, namely all strings of $0$s and $2$s of length greater than or equal to 6.

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(For me $0 \in \mathbb{N}$: adjust to personal taste)

I would read $\{(0+2)^{i+5}|\space i \in \mathbb{N}\}$ as $\{(0+2)^{0+5}, (0+2)^{1+5}, (0+2)^{2+5}, (0+2)^{3+5}, \ldots\}$, i.e. as $\{32,64,128,256 \ldots\}$.

I might wonder why the writer did not just say $\{2^{i+5}|\space i \in \mathbb{N}\}$ but I would not worry too much.

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Probably because, as James commented, the problem is looking at digits, rather than their values as expressions as numbers. –  Rick Decker Aug 31 '12 at 0:59

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