0.9999999999999 = 1
Posted: Sat May 05, 2007 2:25 pm
http://en.wikipedia.org/wiki/.999_%3D_1
[quote]The equality has long been accepted by professional mathematicians and taught in textbooks. In the last few decades, researchers of mathematics education have studied the reception of this equation among students. A great many question or reject the equality, at least initially. Many are swayed by textbooks, teachers and arithmetic reasoning as below to accept that the two are equal. However, they are often uneasy enough that they offer further justification. The students' reasoning for denying or affirming the equality is typically based on one of a few common erroneous intuitions about the real numbers; for example, a belief that each unique decimal expansion must correspond to a unique number, an expectation that infinitesimal quantities should exist, that arithmetic may be broken, an inability to understand limits or simply the belief that 0.999
[quote]The equality has long been accepted by professional mathematicians and taught in textbooks. In the last few decades, researchers of mathematics education have studied the reception of this equation among students. A great many question or reject the equality, at least initially. Many are swayed by textbooks, teachers and arithmetic reasoning as below to accept that the two are equal. However, they are often uneasy enough that they offer further justification. The students' reasoning for denying or affirming the equality is typically based on one of a few common erroneous intuitions about the real numbers; for example, a belief that each unique decimal expansion must correspond to a unique number, an expectation that infinitesimal quantities should exist, that arithmetic may be broken, an inability to understand limits or simply the belief that 0.999