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Author
revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 17474
revolution
Oddity 1:
• 0/number = 0
• number/0 = undefined
• number/number = 1
So what is 0/0

Oddity 2:
• 0^number = 0
• number^0 = 1
So what is 0^0

Now with that in mind, what is (0/0)^(0/0)
02 Mar 2008, 07:55
edfed

Joined: 20 Feb 2006
Posts: 4240
Location: 2018
edfed
how many zeroes there are in zero? one, only one zero in zero.
0/0=1

and number/0 is not undefined, but infinite.
undefined and infinite are the same, as nobody knows the value of infinite, and nobody knows the limit of undefined.

0^0=0
0 to the power of zero means 0*0*0*0 but zero times, instead of four times.
then, zero to the power of zero is equal to zero.
or possible it is equal to 1

number ^ 0 = 1 is a convention, cause of the maths limits.

then, (0/0)^(0/0) is equal to 1

when i say math cannot explain everithing, i don't say bullshit.
02 Mar 2008, 10:05
Tomasz Grysztar

Joined: 16 Jun 2003
Posts: 7755
Location: Kraków, Poland
Tomasz Grysztar
edfed wrote:
when i say math cannot explain everithing, i don't say bullshit.

When your math cannot explain everything, it's high time to re-think or re-design your math.
02 Mar 2008, 11:08
edfed

Joined: 20 Feb 2006
Posts: 4240
Location: 2018
edfed
are you sure?

give us some examples...
02 Mar 2008, 11:19
Borsuc

Joined: 29 Dec 2005
Posts: 2466
Location: Bucharest, Romania
Borsuc
revolution wrote:
Oddity 1:
• 0/number = 0
• number/0 = undefined
• number/number = 1
So what is 0/0
Ahem, it's undefined in the sense that it depends on context. Let's try this different with infinities.

I think everyone knows that infinity is a very huge value, in fact infinitely huge (and it's not a number either!). The problem when asked what is "infinity/infinity" is that it really depends on the context used. If the denominator is a "larger" infinity (it doesn't make sense, does it? but then infinity is not a number, so numbers only "tend" i.e "approach" infinity, but never 'grab' it).

For example:

Code:
``` lim   x/2*x
x->oo    ```
is simply 1/2. Why you ask? The infinity at the denominator is 'twice' as bigger than the one above. Or in other words, no matter what value, no matter how huge it is, is assigned here instead of 'x', it will ALWAYS equal 1/2, no matter what value is introduced (at least, without complicating stuff with '0' or 'infinity' which already cause a lot of "problems").

Same with 0/0 --> whichever happens to be 'closer to 0' in the given context will represent '0' more purely. In fact, you can even replace the above 'x->oo' with 'x->0' and you will get the exact same 1/2.

If you take your time to plot this function in some CAS software, you will notice that it really does "get closer" to 1/2 when it approaches 0 (in fact it should be a constant horizontal line, at 1/2). The thing is that plots are only approximations -- hence why the limit is used. The limit represents the 'value' that the approximation would converge into.

So it is not right to say "what is 0/0" because it is out of context, much as 'he' would be without a subject.

Also keep in mind that the standard "rules" of algebra could also be misleading -- in particular think in calculus without any 'rules' to better understand it.
02 Mar 2008, 16:55
rugxulo

Joined: 09 Aug 2005
Posts: 2341
Location: Usono (aka, USA)
rugxulo
Code:
```                         00000
0    0  0    0  0    0 0     0
0    0  0    0  0    0       0
000000  0    0  000000    000
0    0  0    0  0    0    0
0    0  0    0  0    0
0    0   0000   0    0    0
```
04 Mar 2008, 15:35
edfed

Joined: 20 Feb 2006
Posts: 4240
Location: 2018
edfed
an other example of infinite not very big, but existing and hard to obtain...
the charge of a capacitor via a resistor. like RC=10000 seconds
R=1M C=100µF G=1V at t=0

input voltage as VE from G
output voltage as VS = VC
I is current in the node G,R,C
J is sqrt (-1) = J
w is the angle, function of t.
t is a constant, considered as perfectlly linear. t(t)=1*(1+t) ???
VE = 1V
assume initial VS=VC=0V
then, the current of circuit is the value I=(VE-VS)/R
and then, the voltage on C, VS, is equal to a*i*t +VS
the time constant RC correspond to the time how VS will be 67% augmented from VE-VS.

VS(t)=VE(t)*e (rc)

then lim VS/VE t ->oo = 1V
then as 1 is the image of infinity, the infinity is equal to 1
VS will strictlly never be equal to VE, even in case of perfect resistors, capacitors, generators and wires.

please correct the big english errors i write. that make this post hard to read and understand.
04 Mar 2008, 23:31
bitRAKE

Joined: 21 Jul 2003
Posts: 2940
Location: vpcmipstrm
bitRAKE
revolution wrote:
Oddity 1:
• 0/number = 0
• number/0 = undefined
• number/number = 1
So what is 0/0

0/number * number/0 = 0/0 * number/number = 0/0

My zero is bigger than your zero!
(I don't know if that is a good thing™ or not, lol.)

_________________
05 Mar 2008, 03:07
Borsuc

Joined: 29 Dec 2005
Posts: 2466
Location: Bucharest, Romania
Borsuc
rugxulo wrote:
Code:
```                         00000
0    0  0    0  0    0 0     0
0    0  0    0  0    0       0
000000  0    0  000000    000
0    0  0    0  0    0    0
0    0  0    0  0    0
0    0   0000   0    0    0
```
They told me I was really bad at explaining calculus

why I like it is that you "need" to understand this stuff, not just follow some rules (as in algebra)
05 Mar 2008, 15:30
revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 17474
revolution
Oddity 3:
• number/∞ = 0
• number/number = 1
• ∞/number = ∞
So what is ∞/∞ =
06 Mar 2008, 17:45
edfed

Joined: 20 Feb 2006
Posts: 4240
Location: 2018
edfed
∞/∞ = 1
because ∞ = ∞

revolution: thanks for the ∞ char, now, i think about, can somebody post a message with a lot of symbols, then, llink it via "interresting topics", then, we'll have a symbol bank accessible for all users...because i don't feel to learn them or make it by myself... hehe
06 Mar 2008, 18:51
revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 17474
revolution
edfed: Do you have "Character map" on your windows machine?

Start/Programs/Accessories/System Tools/Character Map
06 Mar 2008, 18:58
edfed

Joined: 20 Feb 2006
Posts: 4240
Location: 2018
edfed
no i don't have installed this, and my cd is crashed... some parts are impossible to read. like char map.

and i cannot scandisk my first partition, don't know why, and it suxxx.
07 Mar 2008, 01:46
revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 17474
revolution
edfed wrote:
∞/∞ = 1
because ∞ = ∞

1. ∞/∞ = 1, and
2. ∞+∞ = ∞, gives
3. (∞+∞)/∞ = 1
4. ∞/∞+∞/∞ = 1
5. 1+1 = 1
6. 2 = 1

07 Mar 2008, 05:50
Borsuc

Joined: 29 Dec 2005
Posts: 2466
Location: Bucharest, Romania
Borsuc
The reciprocal of x, defined as r(x) is:

r(x) = 1/x

Applying it twice we arrive at the original 'x'.

r(r(x)) = x

Now suppose x is 0.

r(x) should be undefined, but applying r(r(x)) we should arrive at the original x, therefore:

r(r(0)) = 0

So then, who's reciprocal equals 0?

1/∞ = 0 like you said.

r(∞) = 0

r(r(x)) = 0

conclusion -> r(x) = ∞

Therefore: 1/0 = ∞

this was done to further show that +0 and -0 are defined (because of no ambiguity at -∞ and +∞).
08 Mar 2008, 13:07
MHajduk

Joined: 30 Mar 2006
Posts: 6038
Location: Poland
MHajduk
Symbols +0 and -0 are defined and equal to 0 (in real numbers set).
08 Mar 2008, 13:16
Borsuc

Joined: 29 Dec 2005
Posts: 2466
Location: Bucharest, Romania
Borsuc
'equal' to 0 as in their absolute values (because they are too small to be measured by their 'signed' values).

But their reciprocals are different
08 Mar 2008, 13:29
revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 17474
revolution
The_Grey_Beast wrote:
'equal' to 0 as in their absolute values (because they are too small to be measured by their 'signed' values).
if |+x| = 0 and |-x| = 0 then x can only be 0.

Last edited by revolution on 08 Mar 2008, 14:18; edited 1 time in total
08 Mar 2008, 14:03
Borsuc

Joined: 29 Dec 2005
Posts: 2466
Location: Bucharest, Romania
Borsuc
Ok, I think I didn't use the right words (and wasn't talking about 'absolute' as in the abs function, doh I forgot about it, sorry).

+0 and -0 are the same (well, too close to even count in normal computations) on almost every operation, except that they have different reciprocals.

But by definition:

-0 < +0

|-0| = |+0|
08 Mar 2008, 14:06
TmX

Joined: 02 Mar 2006
Posts: 822
Location: Jakarta, Indonesia
TmX
Let's review a basic rule : (x^a)/(x^b) = x^(a-b)

So, 0^0 is actualy (0^0)/(0^0), since 0 = 0 - 0 .

Whaaait a minute ....
09 Mar 2008, 09:13
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