Mathematical existence

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In mathematics, existence is logical possibility. To say "There exists a polygon with 7 sides" is to say that a plane figure's having 7 sides does not logically exclude its being a polygon. Since all mathematical "objects" are ideal, "existence" is not construed to mean physical existence.


While "existence" means possibility or non-self-contradiction,"constructibility" refers to describing a specific object of said type. For example "The plane figure with 7 sides all of equal length whose adjacent sides all meet at an angle of 5π/7 radians" describes a specific 7-gon.