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Let's say we have two functions, $f$ and $g$. $f:\mathbb{R}\mapsto [0,1]$ where $0,1$ denote true, false respectively. $f(x)=1$ when $x$ contains any zeroes as a digit; $f(x)=0$ otherwise.
Now let's suppose that $g(x)$ essentially removed all numbers preceding the decimal point and the decimal itself from $x$ (that is, $g(4.5)=5$, $g(e)=71828182\ldots$ etc.).
Would $f(g(\pi))=1$? That is, does the $g(\pi)$ contain any zeroes as a digit? Do you have any evidence to support your claim?
1 Answer
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Yes, of course there is a 0 in the decimal expansion of $\pi=3.1415926535897932384626433832795\underline{0}2884197...$.
