Is any fraction $,{x}big/ {y},$ an ordinal number and if so, does ordinal $,1 = biglbrace0,dots,y – 1big/ybigrbrace,$ instead of $,leftlbrace0rightrbrace,$?
“If (X, <=) is a well ordered set with ordinal number x, then the set of all ordinals < x is order isomorphic to X. This provides the motivation to define an ordinal as the set of all ordinals less than itself. John von Neumann defined a set x to be an ordinal number iff
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If y is a member of x, then y is a proper subset of x.
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If y and z are members of x, then one of the following is true: y = z , y is a member of z, or z is a member of y.
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If y is a nonempty proper subset of x, then there exists a z member of x such that the y intersection z is empty.” (http://mathworld.wolfram.com/OrdinalNumber.html)
