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Dec
23
comment I have learned that 1/0 is infinity, why isn't it minus infinity?
@millimoose - No, $\infty$ isn't a real number, I never said it was. But you can extend the reals to include $\infty$, that's the hyperreals, and then you can define operations which include reals and $\infty$. (Probably not a ring like I claimed earlier; none of the 4 basic operation has an inverse for $\infty$.)
Dec
22
comment I have learned that 1/0 is infinity, why isn't it minus infinity?
@millimoose - The conclusion is correct inasmuch the limit can't be defined if left and right limit are different. That does not imply that it would be defined if they are equal. And $\infty$ + $\infty$ is $\infty$, by definition. $\infty$ is not a number, but that doesn't mean you can't define a ring for it. And operations with reals, like $\infty$ + r = $\infty$. The fact that $\infty$ + $\infty$ = $\infty$ is the reason why $\infty$ - $\infty$ is not defined; you can't find a result which is consistent with the definition for addition.
Dec
21
comment I have learned that 1/0 is infinity, why isn't it minus infinity?
@millimoose - Sorry, I still don't agree. lim(1/x^2) for x->0 is defined: it's +infinity. That may not be a number in R, but it has a defined symbol, for which a limited number of operations are defined. Like infinity + infinity = infinity, but infinity - infinity is not defined. lim(1/x) on the other hand has no defined value, not in R, nor + or -infinity. That's undefined, which is different from + or -infinity.
Dec
19
comment I have learned that 1/0 is infinity, why isn't it minus infinity?
@millimoose - Not sure that's correct. For instance for 1/x^2 both the left limit and right limit for x -> 0 are +infinity. Then the limit is +infinity, so defined.
Dec
19
comment I have learned that 1/0 is infinity, why isn't it minus infinity?
IEEE-754 doesn't have to give infinity as the result of 1/0; it has a type "NaN" (Not a Number) for these cases.
Oct
18
answered general form of difference equation
Oct
18
revised general form of difference equation
formatting, LaTeX
Oct
18
suggested approved edit on general form of difference equation
Oct
14
awarded  Custodian
Oct
14
reviewed Reject Proof problem: Show that $n^2-1$ is divisible by $8$, if $n$ is an odd positive integer.
Sep
29
comment Resources to learn the meaning of any math symbol
@Hagen - I guess Adrián saw it in the document referred to in this answer. Unfortunately this assumes a rather advanced level from the reader, and familiarity with notation, so symbols and operators aren't explained there.
Sep
29
revised What is $x^y$? How to understand it?
fixed units
Sep
29
suggested approved edit on What is $x^y$? How to understand it?
Sep
29
revised How can I find a general formula describing this piecewise function?
removed sig, tried better title
Sep
29
suggested approved edit on How can I find a general formula describing this piecewise function?
Sep
26
comment Steps to Re-Learn Mathematic the right way
You don't want a "complete guide". Today's mathematics covers so many areas that the complete guide wouldn't fit on your bookshelf, let alone that you would have the means to absorb all of it: that's time, and mental capacity. No offense: nobody understands everything in mathematics. It would be a good idea if you would indicate what application of your maths you have in mind.
Sep
20
answered Proof problem: Show that $n^2-1$ is divisible by $8$, if $n$ is an odd positive integer.
Sep
14
awarded  Organizer
Sep
13
revised Finding the values of the real constants such that the limit exists
edited tags
Sep
12
accepted GCD of rationals