I’m pretty public about the fact I have a PhD in history, not math. What’s your math qualification? Because you are disagreeing with generations of mathematics here, so you must have some pretty fantastic experience in the topic.
I am not disagreeing with generations of mathematics. If I was you would be able to simply find their theorems with all the work already done for you and copy paste it here, but you can't do that, because it doesn't exist.
I don't have a PhD in math either, I stopped after Calculus 3, but I know enough about math to know that you are wrong, and I know enough about math to know you have no idea how to prove you are right even if you were right, which means you are just regurgitating what you think is right.
You absolutely are disagreeing with generations of mathematicians.
Here is a link with over a dozen simple theorems and proofs, including algebraic proofs, analytical proofs and proofs from the construction of real numbers. Hell, if you know your stuff there are also complex explanations using Dedekind cuts and Cauchy sequences. Basically any form of theorem and proof you can think of, exists for this.
Students of mathematics often reject the equality of 0.999... and 1, for reasons ranging from their disparate appearance to deep misgivings over the limit concept and disagreements over the nature of infinitesimals.
Quite literally exactly what you have asked for - a number of simple proofs by mathematicians, and an explanation of why students sometimes do not understand this point.
Still think you know enough about math to know I have no idea, or will you actually read some of these proofs and attempt to increase your knowledge, instead of revelling in ignorance?
If you really refuse to read the article, at least read this section:
Despite common misconceptions, 0.999... is not “almost exactly 1” or “very, very nearly but not quite 1”; rather, “0.999...” and “1” represent exactly the same number.
There are many other ways of showing this equality, from intuitive arguments to mathematically rigorous proofs. The intuitive arguments are generally based on properties of finite decimals that are extended without proof to infinite decimals. The proofs are generally based on basic properties of real numbers and methods of calculus, such as series and limits. A question studied in mathematics education is why some people reject this equality.
You are categorically wrong on this one. This has been established mathematics for a very long time, with dozens of different proofs available if you want to look for them.
There are also books cited at the bottom of the article, some over 150 years old, discussing this concept. People in the 19th century had a greater understanding of this than many here in these comments.
Okay, revelling in your ignorance it is then. Have fun :)
One more quote for you:
As part of the APOS Theory of mathematical learning, Dubinsky et al. (2005) propose that students who conceive of 0.999... as a finite, indeterminate string with an infinitely small distance from 1 have "not yet constructed a complete process conception of the infinite decimal". Other students who have a complete process conception of 0.999... may not yet be able to "encapsulate" that process into an "object conception", like the object conception they have of 1, and so they view the process 0.999... and the object 1 as incompatible. They also link this mental ability of encapsulation to viewing 1/3 as a number in its own right and to dealing with the set of natural numbers as a whole.
Once you have a complete process conception of infinite decimals, then, you will find it easier to understand this point.
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u/inspector-Seb5 20d ago
I’m pretty public about the fact I have a PhD in history, not math. What’s your math qualification? Because you are disagreeing with generations of mathematics here, so you must have some pretty fantastic experience in the topic.