We know that first five fibonacci numbers are $\,0,1,1,2,3\,$. Now I want to include them in a set.
But according to Set theory a set cannot have duplicate elements. So, how can I write the set?
Should I write $S = \{0,1,2,3\}$ or should I write $S = \{0,1,1,2,3\}$?
And hence, what will be the number of elements in set of first five fibonacci numbers?
Actually I have got an exam question that says:
$$B=\{x:x \;\text {is a Fibonacci number and}\ x^2 < 64\}$$
Then what is the number of elements in Power set of $B$?
Here is where I need either to include the redundant $1$ or exclude it. Don't know what to do.
You have to exclude it, so
$$B = \{0,1,2,3,5\}$$
is the set with $5$ elements, and consequently the number of elements in its power set is $2^5 = 32$.
You may write $$B = \{0,1,1,2,3,5\}$$ but it is still the same set with only $5$ elements - $0,1,2,3,\text{ and }5$.