Zero

>>8977460
>calls OP a fag while tripfagging
wew lad
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wew lad

l
a
d

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>>8977934
They are both fags, fag

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>>8977409
>textbook makes a distinction between "whole numbers" (with zero) and "natural numbers" (without zero)

>>8977409
>>Textbook implies 0 is not a natural number

Yeah, there's really not much you can do about that clusterfuck.

My recommendation is:

- Whenever you write, use ℕ+ for the set of positive integers, and use ℕ0 for the set of non-negative integers.

- When an author uses ℕ, assume that there's a 50/50 chance that he means ℕ+ or ℕ0. Just chill out about it, don't get judgmental, and simply try to figure out from context which one he means.

It's obviously not an ideal situation -- but it is what it is, so just deal.

>>8978089
Hey, frickin' 4chan filter changed my + and 0 superscripts to non-superscript. They're idiots for putting that filter on /sci/.

Obviously when I say ℕ+ I mean that the + should be superscript.

>>8977409
Shouldn't there be zero discussion in this thread?

What is 0^0 , and why is it 1?

>>8978105

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.

>>8977409
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.

>>8978159
That's not how it works.

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

>>8977409
Zero does not exist in nature.

>>8978874
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?

>>8978110
>>8978105
Good samefagging.

What's infinity to the 0 you cocky cunt?

>>8979048
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

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>>8978105
but that's wrong you knobhead

>>8979411
Take the average of these two, therefore 0^0 = 0

>>8979411
Did I fucking say anything about a limit? No. I asked what 0^0 was.

>>8979048
> what's a thing that isn't a number
Wow you stumped me!

>>8979411
Now try the same with x^0 and -x^0

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>>8978110
>>8978105

>>8979983
0^0 is fucking 1.

>>8978417
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.

>>8978880
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.

>>8977409
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.

>>8977409
>Using [math]\mathbb{N}[/math] and not [math]\mathbb{Z}^{\geq 0}[/math]

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>>8977409

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?

>>8980102
If you have frog pictures saved on your hard drive you're the disease of this site

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>>8978089
>TFW math fags still have no standard for counting.

>>8979437
and 0^x

>>8980111
[math]x = \frac{a}{b}[/math], [math]b\in \mathbb{N}[/math]

>>8979424
>>8979262
Dumb cunts.

Second answer here is correct https://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

>>8980044

How many gfs do I have?

>>8977460
4chan works with axiomatic system where OP is always a faggot

>>8980374
The only circumstance 0^0 depends on is whether you understand basic math. It's 1

>>8980224
It's a fish dummy

>>8980450
See
>>8979411
>basic math
It's abstract math at this point fucking wannabe

http://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.

>>8977409
>This is the Zero (0) discussion thread
>35 replies

failure

>>8977460
>any contrary viewpoints on the matter?

Zero (0)

>>8980934
why are u calling people wannabes and then not using latex?

>>8983188
[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

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>>8979411
seriously dude

>>8977409
>This is the Zero (0) discussion thread

Told you that you were wrong, buddy.

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>>8977409
>obligatory meme about dividing by zero

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

>>8977409
0 aint even a number nig its a conception

>>8977409
>discussing about nothing
>/sci/

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So what is 0/0?

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

>>8984535
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)

>>8984535
>>8984551
Crikey m8s
It's indeterminate, but it's generally undefined
See
>>8980934

>>8977409
0 is not a number. It's a place holder.

>>8984735
Also, prime numbers don't want to be divided into equal integers. The number 1 is a nigger for this reason.

>>8984735

>placeholder

That's null if anything.

>>8980102
>on /sci/
>can't tell fish from a frog

>>8985661
Meant for
>>8980224