| From Wikipedia, the free encyclopedia Jump to: navigation search In mathematics , the recurring decimal , which is also written as or , denotes a real number equal to . In other words, the notations "0.999â¦" and "1" represent the same real number. The equality has long been accepted by professional mathematicians and taught in textbooks. Various proofs of this identity have been formulated with varying rigour , preferred development of the real numbers, background assumptions, historical context, and target audience. In the last few decades, researchers of mathematics education have studied the reception of this equality 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 that each real number has a unique decimal expansion , that nonzero infinitesimal real numbers should exist, or that the expansion of 0.999⦠eventually terminates. | |
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