문제<\/h2>
Ordinal numbers<\/em> are an extension of the set of nonnegative integers. For each nonnegative integer $x<\/mi><\/mrow>x<\/math><\/span><\/span> x<\/span><\/span><\/span><\/span>, we will establish the corresponding ordinal number f<\/mi>(<\/mo>x<\/mi>)<\/mo><\/mrow>f (x)<\/math><\/span><\/span> f<\/span> (<\/span> x<\/span>)<\/span><\/span><\/span><\/span>. The first few ordinal numbers can be defined as follows.<\/p> Zero corresponds to an empty set: f<\/mi>(<\/mo>0<\/mn>)<\/mo>=<\/mo><\/mrow>f(0) = <\/math><\/span><\/span> f<\/span> (<\/span> 0<\/span>)<\/span> <\/span> =<\/span><\/span><\/span><\/span> {}<\/code>.<\/li> One corresponds to the set containing the set f<\/mi>(<\/mo>0<\/mn>)<\/mo><\/mrow>f (0)<\/math><\/span><\/span> f<\/span> (<\/span> 0<\/span>)<\/span><\/span><\/span><\/span> as an element: f<\/mi>(<\/mo>1<\/mn>)<\/mo>=<\/mo><\/mrow>f(1) = <\/math><\/span> Two corresponds to the set containing the sets f<\/mi>(<\/mo>0<\/mn>)<\/mo><\/mrow>f (0)<\/math><\/span><\/span> f<\/span> (<\/span> 0<\/span>)<\/span><\/span><\/span><\/span> and f<\/mi>(<\/mo>1<\/mn>)<\/mo><\/mrow>f (1)<\/math><\/span> And so on: each positive integer k<\/mi><\/mrow>k<\/math><\/span><\/span> k<\/span><\/span><\/span><\/span> corresponds to the set containing all the previous ordinal numbers as elements. The formula is: f<\/mi>(<\/mo>k<\/mi>)<\/mo>=<\/mo><\/mrow>f(k) = <\/math><\/span><\/span> f<\/span> (<\/span> k<\/span>$

Ordinal Number