Addition of Natural and Real Numbers
To prove the usual properties of addition, one must first define addition for the context in question. Addition is first defined on the natural numbers. In set theory, addition is then extended to progressively larger sets that include the natural numbers: the integers, the rational numbers, and the real numbers. (In mathematics education, positive fractions are added before negative numbers are even considered; this is also the historical route)
Read more about this topic: Addition
Famous quotes containing the words addition of, addition, natural, real and/or numbers:
“The addition of a helpless, needy infant to a couple’s life limits freedom of movement, changes role expectancies, places physical demands on parents, and restricts spontaneity.”
—Jerrold Lee Shapiro (20th century)
“The addition of a helpless, needy infant to a couple’s life limits freedom of movement, changes role expectancies, places physical demands on parents, and restricts spontaneity.”
—Jerrold Lee Shapiro (20th century)
“The common notions that we find in credit around us and infused into our souls by our fathers’ seed, these seem to be the universal and natural ones. Whence it comes to pass that what is off the hinges of custom, people believe to be off the hinges of reason.”
—Michel de Montaigne (1533–1592)
“A scholar, in his Segmenta, left a note,
As follows, “The Ruler of Reality,
If more unreal than New Haven, is not
A real ruler, but rules what is unreal.””
—Wallace Stevens (1879–1955)
“I’m not even thinking straight any more. Numbers buzz in my head like wasps.”
—Kurt Neumann (1906–1958)