All Questions
Tagged with real-numbers functions
19
questions
7
votes
4
answers
1k
views
Is any real-valued function in physics somehow continuous?
Consider the following well-known function:
$$
\operatorname{sinc}(x) = \begin{cases} \sin(x)/x & \text{for } x \ne 0 \\
1 & \text{for } x =0 \end{cases}
$$
In physics, the sinc function has ...
- 17.2k
2
votes
1
answer
272
views
Change of coordinate codomain from $[-1,1]$ to $[0,1]$
How does one translate coordinates from $[-1,1]$ to $[0,1]$? That is, suppose we have an ordered pair $(x,y)$ which lies between $[-1,1]$ and want to push into the range delimited by $[0,1]$.
A lot ...
10
votes
3
answers
1k
views
Significance of Codomain of a Function
We know that Range of a function is a set off all values a function will output.
While Codomain is defined as "a set that includes all the possible values of a given function."
By knowing ...
- 386
8
votes
3
answers
2k
views
Is there a bijective, monotonically increasing, strictly concave function from the reals, to the reals?
I can't come up with a single one.
The range should be the whole of the reals. The best I have is $\log(x)$ but that's only on the positive real line. And there's $f(x) = x$, but this is not strictly ...
- 203
3
votes
2
answers
89
views
How can i find the domain of $f(x)$= $x^{1/x}$ on the negative numbers?
I have been thinking of which negative values of $x$ yield a real number when plugged on $f(x)$ = $x^{1/x}$,
It is clear to see that it does not work for negative even numbers
$(-2)^{-1/2}$ = $(\...
17
votes
8
answers
7k
views
Can we have a one-one function from [0,1] to the set of irrational numbers?
Since both of them are uncountable sets, we should be able to construct such a map. Am I correct?
If so, then what is the map?
- 6,016
8
votes
2
answers
1k
views
Info on the locale of surjections from the Natural Numbers to the Real Numbers
On the nlab page for locales, it states that there is locale for the surjections from the Naturals to the Reals. This locale has no points (i.e. elements), since there are no such surjections, but the ...
- 10.5k
8
votes
3
answers
20k
views
What does $R \rightarrow R$ means in functions?
I have a function.
The function is:
$$ f:R \rightarrow R $$
$$ f(x) = x^3$$
What does $R \rightarrow R$ means?
I don't know what types of questions should I ask here. If it is not ok, the I will ...
- 145
8
votes
4
answers
1k
views
Are logarithms the only continuous function on $(0, \infty)$ such that $f(xy) = f(x) + f(y)$?
Are logarithms the only continuous function on $(0, \infty)$ that has this property?
$$
f(xy) = f(x) + f(y)
$$
If so, how would we show that? If not, what else would we need to show that a function $...
- 2,323
5
votes
2
answers
168
views
Existence of Function Taking Every Value Uncountably Many Times
I am stuck on the following problem coming from a plane geometry theorem I'm working on. This is a generalization of that problem which might actually prove easier to handle. All the techniques that ...
- 223
4
votes
3
answers
5k
views
Is $\frac{1}{x}$ a function?
Consider $f(x)=\frac{1}{x}$ defined on set of real numbers.
If every element in domain has image, then above relation is said to be a function.
But for $x=0$, $f(x)=\text{infinity}$.
Does it mean ...
- 91
4
votes
3
answers
1k
views
If $a$ and $b$ are roots of $x^4+x^3-1=0$, $ab$ is a root of $x^6+x^4+x^3-x^2-1=0$.
I have to prove that:
If $a$ and $b$ are two roots of $x^4+x^3-1=0$, then $ab$ is a root of $x^6+x^4+x^3-x^2-1=0$.
I tried this :
$a$ and $b$ are root of $x^4+x^3-1=0$ means :
$\begin{cases}
a^4+...
- 217
3
votes
1
answer
4k
views
Bijection from the irrationals to the reals
Since the irrationals and the reals have the same cardinality, there must be a bijection between them. Somewhere on this forum I found something like this:
Map all of the numbers of the form $q + ...
- 3,709
3
votes
1
answer
146
views
Find closest whole integer in equation
Given the following equations:
$$a=\frac{py+qx}{2pq}$$
$$b=\frac{py-qx}{2pq}$$
Where p and q are some real constant number. And $(x, y)$ are some arbitrary real number. Any number can be inputted as ...
- 53
2
votes
1
answer
1k
views
Why is this not a function?
This problem is from Discrete Mathematics and its Applications
This is the definition that the book gave of function
Here is my work so far
It's pretty clear to me that 1b and 1c are not functions ...
- 1,884