Tagged Questions
1
vote
1answer
41 views
Can we write $\sqrt[w]{z}=z^\frac{1}{w}$ when both $w$ and $z$ are complex numbers? [duplicate]
Let $w$ and $z$ be complex numbers defined in terms of real numbers $a$, $b$, $c$ and $d$ as follows:
$$ w = a+bi \\ z = c+di $$
Can we analogically write
$$ \sqrt[w]{z} = z^\frac{1}{w} \qquad ...
4
votes
2answers
102 views
How to evaluate powers of powers (i.e. $2^3^4$) in absence of parentheses?
If you look at $2^{3^4}$, what is the expected result? Should it be read as $2^{(3^4)}$ or $(2^3)^4$? Normally I would use parentheses to make the meaning clear, but if none are shown, what would you ...
8
votes
6answers
372 views
Can anyone explain why $a^{b^c} = a^{(b^c)} \neq (a^b)^c = a^{(bc)}$
I'm so puzzled about this:
$$a^{b^c} = a^{(b^c)} \neq (a^b)^c = a^{(bc)}.$$
Why isn't $a^{b^c}$ equal to $a^{(bc)}$? Why is $a^{b^c}$ instead equal to $a^{(b^c)}$? And how is it possible that ...
0
votes
2answers
67 views
Exponentation vs Power
What definition of $a^b$ operation is the most popular and standartized: Exponentation or Power?
Is any difference between them?
1
vote
0answers
115 views
Notation for Cartesian power, an oddity in the international standard
The Cartesian product of $A$ with itself $n$ times is normally denoted using superscript notation $A^n$, and this what ISO 31-11 defined as standard. However, ISO 31-11 has been superseded by ISO ...
2
votes
3answers
156 views
Mathematical function for the powers
I have this formula $$\underbrace{2^{2^{2^{.^{.^{.^{2^2}}}}}}}_n$$i.e. where the total number of 2's is $n$.
Is there any way to write it as a single mathematical function?
9
votes
3answers
532 views
Who introduced the notation $x^2$?
In the book 'Problem Solving and Number Theory' I read
The law of quadratic reciprocity was discovered for the first
time, in a complex form, by L. Euler who published it in his paper
...
