bi·jec·tion (b?-j?k?sh?n)n. Mathematics A function that is both one-to-one and onto.[bi- + (in)jection or (pro)jection.]American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.bijection (ba??d??k??n) n (Mathematics) a mathematical function or mapping that is both an injection and a surjection and therefore has an inverse. See also injection5, surjectionCollins English Dictionary ? Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014