The discussion centers on the mathematical equality 0.999... = 1, addressing student misconceptions regarding infinity and its implications in mathematics. Participants argue that students often perceive 0.999... as a finite number of nines rather than an infinite series, leading to confusion. The conversation highlights the necessity of teaching concepts like convergence and limits to clarify these misunderstandings. Furthermore, it emphasizes that mathematical constructs do not need to correspond to physical reality, as demonstrated by the historical context of non-Euclidean geometry.
PREREQUISITESMathematics educators, students grappling with concepts of infinity, and anyone interested in the philosophical implications of mathematical truths.
coolul007 said:The point that I try to make is that a limit is NOT equality. A limit is a number that will not be reached and will not go beyond, because one can always add an iteration to the sequence. The fact that limits have been used so much to achieve success, doesn't mean that they are EQUAL. We also treat pi and e as if they were not limits, but numbers, nice habit, but not accurate.
I think that you have a fundamental misunderstanding of what a limit actually means, based on what you are saying above, particularly the part about "that will not be reached".coolul007 said:A limit is a number that will not be reached and will not go beyond, because one can always add an iteration to the sequence.
coolul007 said:The point that I try to make is that a limit is NOT equality. A limit is a number that will not be reached and will not go beyond, because one can always add an iteration to the sequence. The fact that limits have been used so much to achieve success, doesn't mean that they are EQUAL. We also treat pi and e as if they were not limits, but numbers, nice habit, but not accurate.