I just want a function f(x) = 1,0,0,0,0,0,... where x eof N

I just want a function f(x) = 1,0,0,0,0,0,... where x eof N

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Why not?

0^x?

[math]f(0)=1, f(n)=f(n-1)*0 n>0[/math]

im searching for a solution thats not a recursion and does not use < or > or if

this is what im looking for but Wolfram alpha says 0^x is undefinded but google says its ok wat do

[eqn] f(n) = \frac{d^n}{dx^n} 1 [/eqn]

0^0 is undefined. You're in trouble if you want to describe your function without recursion or ifs. The last resort is using special functions such as floor, ie [math] f(n) = floor(1/(n+1)) [/math]

>0^0 is undefined.
What if I want to use it in a proof? Can I just define it or will people get pissed?

f(n)=1-min(1,n)

Try it out and see if they get pissed or not

>I just want a function f(x) = 1,0,0,0,0,0,... where x eof N
Well, a function is defined precisely once its domain is specified along with the value it assigns to each element of the domain.
Which is exactly what you've just done so there's no issue at all.

these are the only sane answers

floor is cheating, min is cheating

hardcoing values is cheating

>0^0
>sane

[math] f(x)={\begin{cases}1&{\mbox{if }}x\in \{ 0 \},\\0&{\mbox{if }}x\notin \{ 0 \}.\\\end{cases}} [/math]

Why use sets instead of equality (to zero) ?

no if allowed bro

sgn(x+1) - sgn(x)

[math]f(n) = \delta(n)[/math]

you must be atleast 18 years old to post on this board.

sin(2^(x-1)*pi)

Did I offend you?

Nice

>is undefined
No, [math] 0^0 = 1 [/math].

my man

thanks

No, undefined. Consider for example:
[math]
0^2 : 0^2 = 0^0
[/math]

Go back to you imbecile. You can't divide by 0.
[math] 0^0 [/math] is an empty product, so it's equal to 1.

That's like saying 0^3 is undefined because
[eqn] 0^5 : 0^2 = 0^3 [/eqn]

>dividing by 0

[math]\sum_{d|n+1}\mu(d)[/math]

>[math]0\in\mathbb{N}[/math]

i think this works
[eqn]f(x)=\lim_{k\to\infty}\exp\left({-\sum_{n=0}^{k}x^n }\right) [/eqn]

That's exactly what the second poster was pointing out.

[math]\displaystyle f(x)=\frac{\prod_{k}(x-k)}{-\prod_k k}[/math]

Bro your smart

>math.hmc.edu/funfacts/ffiles/10005.3-5.shtml

mathforum.org/dr.math/faq/faq.0.to.0.power.html

[math]f(x) = -\prod \limits_{i = 0}^x \left( i - 1 \right)[/math]

(where [math]0 \in \mathbb{N}[/math])

nice

[math]\displaystyle f(x)=\lim_{k\,\to\ x\pi}\frac{\sin k}{k}[/math]

this "functions can only be closed-form expressions" meme needs to die

you need to die

kys

Im sure theres a better way to do this, but
let [math]\mathcal{M_{xx}(1)}[/math] denote an [math]x\times x[/math] matrix populated by 1s. then let [math]f(x)=1-|\mathcal{M}_{xx}(1)|[/math]

This is the definition of delta_{1,x}, just use that.

Let f(x) be the probability that neither a head nor tails is obtained after x coin flips