Zero

Because you have zero factors of zero, and 1 is the base on which all natural numbers are grown by tacking on factors. Freaking novice, I'm a mathematician so I'm too good to be here most of the time but I like to come and tell you I'm better.

In the Fibonacci sequence there is no zero because something (numbers) cannot be derived from nothing. Zero implies nothing, no sum, no quantity which is illogical in nature. Much like how our universe logically could not be derived from nothing and how time cannot be derived from nothing. If you have zero minutes at the universes start and you add zero minute of time for it to be born in, nothing will happen ever. Therefore 0 is not a "natural" number.

That's not how it works.

>textbook uses N for {1, 2, 3,...} and {0, 1, 2, 3,...} interchangeably

Zero does not exist in nature.

It does. How many fucks do I give about (you)?

Also, zero is even
Deal with it.

At what point is there a purpose for defining zero as a natural number or not? Is there any study of math that the solutions to problems are greatly affected by including or excluding 0 as a natural number?

Good samefagging.

What's infinity to the 0 you cocky cunt?

Nothing, infinity is not a number, so you can't raise it to a power

The limit of n^0 as n goes to infinity is 1 however

but that's wrong you knobhead

Take the average of these two, therefore 0^0 = 0

Did I fucking say anything about a limit? No. I asked what 0^0 was.

> what's a thing that isn't a number
Wow you stumped me!

Now try the same with x^0 and -x^0

...

0^0 is fucking 1.

No, that is how it works. Everything in nature tells us via pressure mediation/harmonics, and it is always moving. There is NO nothing. There is NO zero. There is a starting point of "1" and the after images of 1.

Where in nature? Absolute zero? There is no absolute zero. There is always something. It is in no way shape or form a natural number and the fact that we use it is arguably irrational and illogical. Not even the Greeks used zero, they had no number for it. Infinity and zero are considered at best to be "indeterminate forms".
Please tell me where in nature or even the universe where I can find a "zero" and once you find it then you can proceed to no longer exist on this plane of existence.

I prefer not to count zero as a natural number simply because to me the natural numbers are supposed to be the most primary, fundamental set of numbers that math is used for and historically the concept of 0 was never incorporated into a number system until long after there was a system for counting all nonzero natural numbers (and in many cases, all positive rational numbers). Therefore there is clearly something about 0 that sets it apart from the "other" natural numbers, even if it doesn't seem that way from our modern perspective.

>Using [math]\mathbb{N}[/math] and not [math]\mathbb{Z}^{\geq 0}[/math]

...

When does it matter in mathematics whether or not 0 is or isn't a natural number? When does 0 being or not being a natural number affect solutions on mathematic problem solving?

If you have frog pictures saved on your hard drive you're the disease of this site

>TFW math fags still have no standard for counting.

and 0^x

[math]x = \frac{a}{b}[/math], [math]b\in \mathbb{N}[/math]

Dumb cunts.

Second answer here is correct math.stackexchange.com/questions/714170/what-is-infinity-to-the-power-zero

Like 0^0 it depends on the circumstances and definitions

Kill yourselves to stop dragging down the average intelligence

How many gfs do I have?

Veeky Forums works with axiomatic system where OP is always a faggot

The only circumstance 0^0 depends on is whether you understand basic math. It's 1

It's a fish dummy

See
>basic math
It's abstract math at this point fucking wannabe

en.wikipedia.org/wiki/Indeterminate_form

There is no universal value for ∞^0. It is indeterminate, and the value depends on how you are getting the ∞ and the 0. Some other indeterminate forms are 0/0,1^∞,∞×0,0^0. I might have missed a few.

For example consider the function f1(n)=(1+1/n)n . At ∞ it is of the form 1^∞ , but

lim n→∞ f(n)=e≈2.718⋯

Now consider f2(n)=(1+2/n)n . At ∞ this is also of the form 1^∞ but the limit is,

lim n→∞ f(n)=e2≈7.389⋯

∑∞ i=1 k^(1/k)
is infinite since you are adding a non-zero constant (k^(1/k)) to itself an infinite number of times.

If we change the summation to ∑∞ i=1 i^(1/i), this is still infinite as although the terms are not constant, each of them is greater than 1 and so the series is greater than 1+1+1+⋯ , therefore infinite (no it's not -1/2 in this case).

As to why each term is greater than 1
, the function f(x)=x^(1/x) is monotonically decreasing ∀x>e, and each term must be greater than the limit of the function at ∞ , and this limit

lim n→∞ n^(1/n)=1

As to why this limit is 1, (and why the other limits are e and e2 respectively) this is a topic too broad for the scope of this answer. I suggest you read the article linked above, and also read a good book on calculus, in case you are willing to self-study.

>This is the Zero (0) discussion thread
>35 replies

failure

>any contrary viewpoints on the matter?

Zero (0)

why are u calling people wannabes and then not using latex?

[spoiler]because I'm a wannabe[/spoiler]
But really I'm not familiar with this sites math script. I've tried looking it up for a bit, yet there's many mixed results

seriously dude

>This is the Zero (0) discussion thread

Told you that you were wrong, buddy.

>obligatory meme about dividing by zero

Now that THAT is out of the way, back to your regularly scheduled thread, already in progress.

0 aint even a number nig its a conception

>discussing about nothing
>Veeky Forums

So what is 0/0?

I used to think it was 0 but I'm starting to believe it is actually infinity

Anything divided by 0 is 0

the number of people in this thread who seem to have a basic understanding of set theory is 0 (zero)

Crikey m8s
It's indeterminate, but it's generally undefined
See

0 is not a number. It's a place holder.

Also, prime numbers don't want to be divided into equal integers. The number 1 is a nigger for this reason.

>placeholder

That's null if anything.

>on Veeky Forums
>can't tell fish from a frog

Meant for