Editing Surreal number (section)

===Examples===
The surreal exponential is essentially given by its behaviour on positive powers of {{mvar|ω}}, i.e., the function {{tmath|g(a)}}, combined with well-known behaviour on finite numbers. Only examples of the former will be given. In addition, {{tmath|1=g(a) = a}} holds for a large part of its range, for instance for any finite number with positive real part and any infinite number that is less than some iterated power of {{mvar|ω}} ({{mvar|ω{{sup|ω{{sup|·{{sup|·{{sup|ω}}}}}}}}}} for some number of levels).
* {{math|1=exp ''ω'' = ''ω''{{sup|''ω''}}}}
* {{math|1=exp ''ω''{{sup|1/''ω''}} = ''ω''}} and {{math|1=log ''ω'' = ''ω''{{sup|1/''ω''}}}}
* {{math|1=exp (''ω'' · log ''ω'') = exp (''ω'' · ''ω''{{sup|1/''ω''}}) = ''ω''{{sup|''ω''{{sup|1 + 1/''ω''}}}}}}
** This shows that the "power of {{mvar|ω}}" function is not compatible with {{math|exp}}, since compatibility would demand a value of {{mvar|ω{{sup|ω}}}} here
* {{math|1=exp ''ε''{{sub|0}} = ''ω''{{sup|''ω''{{sup|''ε''{{sub|0}} + 1}}}}}}
* {{math|1=log ''ε''{{sub|0}} = ''ε''{{sub|0}} / ''ω''}}