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1:10 Could they be considered to be different parts of the same real number?
1:30 Summation Notation; lower part and upper part.
2:05 Any algorithm that can produce an infinite string of zeros... Infinite zeros exists as a concept, but infinite 9's does not????
3:20 Choice of representations: Start with 0 or start with 1
3:45 The arithmetical argument
4:20 1/9 does not have a terminating decimal expression.
4:50 In base 3, 1/9 has both terminating and nonterminating expression. (Dual representation.)
5:50 Representing the right side and the left side of a real number.
6:10 limit as x approaches from the left, and from the right.
6:40 Common convention: Just disallow the question... If there is an infinite discontinuity in the graph, you just don't get to ask what the function is equal to AT the point of discontinuity.
7:30 Every number x has a left hand side x+(-0) and a right hand side: x+(+0); It's the same real number, but there are two sides to every number.
9:00 Graph of 1/x
9:30 Definition of +0 and -0, using summation notation given any base n > 1
10:50 Roy Tomes: Agrees, since 1/0+ not equal 1/0-, the two numbers must be different.
11:10 Conventional mathematics "Don't think of it that way. We'll remove 0 from the domain of 1/x"
12:25 You can approach a door from the left or right.
12:40 David Eaton: IEEE standards
13:00 Coelacanth, A field; Once you add infinity to a set, it is not a field.
13:10 The unit step function's ambiguous value at t=0.
14:00 (Extended Real Number Line) Property treats +0 and -0 as the same, while +infinity and -infinity are different. (No other reason, I don't think, than because they wanted to define it that way.)
14:50 A lousy argument on wikipedia... Since there ARE functions whose value is ambiguous at x=0, (output a range of values) we decide we will treat ALL functions as though the output is ambiguous.
15:20 Typo in wikipedia. The sinc function does not have an ambiguous value at 0.
15:50 sin(1/x) is much more interesting, and really becomes undefined at x=0.
16:25 u(x) and 1/x provide unambiguous values around 0
17:10 Atomic-S question of plotting complex-valued functions arounc zero, and graph of real part and imaginary part of 1/(a+bi)
