meta user
network profile
| bio | website | |
|---|---|---|
| location | ||
| age | ||
| visits | member for | 2 years, 7 months |
| seen | 2 hours ago | |
| stats | profile views | 487 |
|
Nov 4 |
comment |
Zero to the zero power - Is $0^0=1$? 0^0 is undefined by whom? I saw somebody defined it, can I now say it is defined? |
|
Nov 4 |
comment |
Zero to the zero power - Is $0^0=1$? "otherwise it would lead to all sorts of exceptions when dealing with the limit laws" - can you please give some examples of such exceptions? |
|
Nov 4 |
accepted | What is the value of $\lim_{x\to 0} x^i$? |
|
Nov 4 |
comment |
What is the value of $\lim_{x\to 0} x^i$? So the limit of the absolute value is 1 and the limit of the argument in infinity, right? |
|
Nov 4 |
comment |
What is the value of $\lim_{x\to 0} x^i$? there is a link in the question tinyurl.com/ckwmayc |
|
Nov 4 |
comment |
What is the value of $\lim_{x\to 0} x^i$? Thanks, but what does mean the result which Wolfram Alpha returns? |
|
Nov 4 |
comment |
What is the value of $\lim_{x\to 0} x^i$? @amWhy it is insane because it is neither an algebraic expression, nor indeterminacy. |
|
Nov 4 |
comment |
What is the value of $\lim_{x\to 0} x^i$? @DonAntonio I do not want to boost the accept rate by accepting answers that do not answer my questions or by asking easy, elementary questions. |
|
Nov 4 |
comment |
What is the value of $\lim_{x\to 0} x^i$? @did I do not know, but many of the questions I ask indeed difficult. |
|
Nov 4 |
comment |
What is the value of $\lim_{x\to 0} x^i$? @DonAntonio I usually ask difficult questions that little people can answer. I prefer asnwering easy questions myself. |
|
Nov 4 |
asked | What is the value of $\lim_{x\to 0} x^i$? |
|
Nov 1 |
comment |
In dual numbers, what is the value of expressions $0^\varepsilon$ and $\varepsilon^{\varepsilon}$? @Micah this is interesting information, it would be great if you could summarize this as an answer. |
|
Nov 1 |
comment |
In dual numbers, what is the value of expressions $0^\varepsilon$ and $\varepsilon^{\varepsilon}$? @Micah that is I was asking about. Whether the limits exist and whether they agree in all directions. |
|
Nov 1 |
comment |
In dual numbers, what is the value of expressions $0^\varepsilon$ and $\varepsilon^{\varepsilon}$? well at least any smooth function of one argument can be extended to dual numbers as well following the rule: $f(a+b\varepsilon)=f(a)+f'(a)b\varepsilon$. So $p^{a+b\varepsilon}=p^a+p^a \ln p \varepsilon$ and $(a+b\varepsilon)^p=a^p+p a^{p-1} b \varepsilon$ so the both notions of exponentiation are well defined for the most of the dual numbers. |
|
Nov 1 |
comment |
In dual numbers, what is the value of expressions $0^\varepsilon$ and $\varepsilon^{\varepsilon}$? After all if such things would not be defined there, the set possibly would not be called a number set. |
|
Nov 1 |
comment |
In dual numbers, what is the value of expressions $0^\varepsilon$ and $\varepsilon^{\varepsilon}$? I see your point but I believe that the dual numbers are defined enough well so that exponentiation $x^y$ (in non-boundary cases) is defined. Am I wrong? Does square function of constant e differ in dual numbers from exp(2)? |
|
Nov 1 |
comment |
In dual numbers, what is the value of expressions $0^\varepsilon$ and $\varepsilon^{\varepsilon}$? @Steven Stadnicki why not? Exponentiation is defined there |
|
Nov 1 |
asked | In dual numbers, what is the value of expressions $0^\varepsilon$ and $\varepsilon^{\varepsilon}$? |
|
Oct 30 |
comment |
A definable hyperreal system @Ian Mateus yes this is exactly what I saw before making this question. |
|
Oct 30 |
asked | A definable hyperreal system |
