Why Does This Probability Equation Evaluate to 0.5?

[tntcoder]

Hi,

Please can someone explain to me how this probability equation evaluates to 0.5

\frac{2^{f(n)+2}}{2^{f(n)+1}} = \frac{1}{2}

f(n) is essentially anything in this context.

For me the probability evaluates to 2, but this is straight out a research paper and I can't doubt their maths.

This is the context:

Because there are 2^{f(n)+2} texts with length f(n)+2, the probability for a selected text with length f(n)+2 having a related
compressed text of length ≤ f(n) is less than \frac{2^{f(n)+2}}{2^{f(n)+1}} = \frac{1}{2}

Please can someone explain to me where the 0.5 comes from? I can see if i turn the equation upside down it works, but I am guessing its not that simple :p

 

[statdad]

Make sure you've typed things correctly - otherwise the expression seems to be the reciprocal of what it should be.

<br /> \frac{2^{f(n)+2}}{2^{f(n)+1}} = \frac{2 \times 2^{f(n)+1}}{2^{f(n)+1}} = 2<br />

If the original expression is the reciprocal of what you've typed, the expression does
reduce to 1/2