• Journal of the Chungcheong Mathematical Society
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• v.24 no.4
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• pp.675-686
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• 2011

The aim of this paper is two fold: One of them is to introduce a formal definition of ordinals which is equivalent to Neumann's definition without assuming the axiom of regularity. The other is to introduce the weak transfinite set and show that the weak transfinite set is a transfinite limit ordinal.