Meanderings : 7,000 posts

[Black Mage]

oo is infinitely big
1/oo is infinitely small
0 is the absence of anything
only one can be measured
only one can be used as a mathematical value

but, some calculaors use oo to go around the 'error: overflow' bit

what does teh calculatar say?

[Niteowl]

WTH!?!? i leave yONE post alone, i don't read it. JUST ONE!! and you guys go CRAZAY ON ME!!! sheeesh!

[Keyser59]

*ahem*
http://mathforum.org/library/drmath/view/62486.html

This guy explains it well. Infinity is a concept used when exploring calculus, not a number.

(BTW I'm not Kaiser)

[a civilian]

That is the one oddball example where nothing really holds true, just because of the fact 0 divided by 0 is undefined.

In pretty much every other example this holds true. If f(0) = 3, the closer and closer your x values come to 0, the closer and closer your f(x) values will come to 3. Unless you have a jump discontinuity, the value of a function will always be the same as the limit.

Simulating zero with increasingly small numbers also fails to work when multiplying it by infinity (assuming infinity is always simulated with a number that is equally large as the number that is used to simulate zero is small, or assuming infinity is truly infinite).  Likewise, simulating infinity with increasingly large numbers works in all situations except multiplication of it by zero and division of it by itself.

Infinity may not be already defined as a number, but if that is the case then I am defining infinity as a number.

And Black Mage, your calculator tells me exactly what I want to see (oo * 0 = undefined).

[Uranium - 235]

My god you people go so off-topic with this crap... I think we need to make meandering threads, then seal the doors and gas everyone that posted in it :p

[a civilian]

I think we need to make meandering threads, then seal the doors and gas everyone that posted in it :p

That group would seem to include you.

[Keyser59]

Ok, after rethinking my calculus a bit I have figured that there are examples where infinity times 0 can be 1, 0, or infinity.

The only examples I could come up with were when it equals 0.

lim (x -> 0) [ e^x / x! ] = 0
or
lim (x -> 0) [ x * ln(x) ] = 0

finally I looked at lim (x -> oo) [ x * 1/x ] = 1

So yes, infinity times zero is in fact undefined.

But 0 is still not the reciprocal of infinity, and 1/0 is a null set.

[a civilian]

Infinity may not be already defined as a number, but if that is the case then I am defining infinity as a number.

To clarify on this, I do not see why it cannot be regarded as a number.  Undefinable?  Just as you could say one represents a single object and zero represents no objects, you could say infinity represents an infinite number of objects.  Intangible?  Zero is no more tangible than infinity.

[Black Mage]

proof that infinity is not a number:
i have an infinitum of apples
i split it among all lm slot holders
civ, how many apples do you have?
<a civilian> errr ... an infinite amount?
so if i started with oo apples and i have all the slotholders an equal amount of apples (say there are 20) and they each have oo
1 * oo = 20 * oo
divide by oo (since oo is, for this experiment an algebraic quantity)
1 = 20
true

and if you were to say that:
1 * oo = 20 * oo
simplify
oo = oo
true

that proves that oo can not be an algebraic number, as 20 * oo can not equal oo because 20 is not the number of multiplicative identity

as far as algebra goes, oo is a concept and i'm going to find the ascii keystroke-sequence-thing for it so we can actually have the character

[a civilian]

[edit]This is not a reply to Black Mage.[/edit]

In 1/x, plugging in increasingly low numbers to simulate zero will result in increasingly high numbers for the quotient.  This indicates that when zero is plugged in, the operation will yield an infinite result.  Is this not so?

[a civilian]

And in reply to Black Mage, that is not sufficient proof; I could use the exact same method to prove that zero is not a number.

[Black Mage]

there appears to be an infinity chatachter in times new roman, but not an alt-keycode for it
this should be it: ∞ (copy + paste)

and in reply to civ

but i never gave any apples to any regs
1 * 0 = 20 * 0
through the multiplicative zero property as:
1 * 0 = 0
20 * 0 = 0

infinity is not an algabraic quantity as it cannot be quantified or counted

calculus deals with infinitums but most real world math is algebra
1 + 1 = x, etc


<-- begin somewhat large algebraic proof -->

#1, real values

∞ > everything
20 * ∞ = ∞
1 * ∞ = ∞
20 > 1
(20 * ∞) > (1 * ∞)

by defenition ∞ is:
for any real x
∞ = x + 1
therefore anything less than infinity is x
x is real

20 > 1
(20 * ∞) > (1 * ∞)
20 * ∞ = ∞
1 * ∞ is less than ∞
1 * ∞ is therefore real
false

#2 simple algebra

20 * ∞ = 1 * ∞
for any a*b = c*d
a/d = c/b
therefore
20/∞ = 1/∞
reduce
20 = 1

<-- begin somewhat large algebraic proof -->

the second is easier to understand

oh and on topic: as of this posting we have 7,883 posts
well on our way to yet another discussion about finite math!

[a civilian]

∞ > everything
20 * ∞ = ∞
1 * ∞ = ∞
20 > 1
(20 * ∞) > (1 * ∞)

by defenition ∞ is:
for any real x
∞ = x + 1
therefore anything less than infinity is x
x is real

20 > 1
(20 * ∞) > (1 * ∞)
20 * ∞ = ∞
1 * ∞ is less than ∞
1 * ∞ is therefore real
false

Allow me to reword:

0 < all positive real numbers
20 * 0 = 0
1 * 0 = 0
20 > 1
(20 * 0) > (1 * 0)

by definition 0 is:
for any positive real number x
0 = 1/(x + 1)
therefore anything greater than zero is x
x is nonzero

20 > 1
(20 * 0) > (1 * 0)
20 * 0 = 0
1 * 0 = 0
0 > 0
0 is therefore nonzero
false

20 * ∞ = 1 * ∞
for any a*b = c*d
a/d = c/b
therefore
20/∞ = 1/∞
reduce
20 = 1

20 * 0 = 1 * 0
for any a*b = c*d
a/d = c/b
therefore
20/0 = 1/0
reduce
20 = 1

[JHunz]

Allow me to reword:

0 < all positive real numbers
20 * 0 = 0
1 * 0 = 0
20 > 1
(20 * 0) > (1 * 0)

by definition 0 is:
for any positive real number x
0 = 1/(x + 1)
Wrong.  For any real number x, 1/(x+1) is nonzero.  Therefore the rest of this proof is useless
therefore anything greater than zero is x
x is nonzero

20 > 1
(20 * 0) > (1 * 0)
False.  This inequality is only valid for positive numbers.  Zero is not a positive number.  Therefore the rest of this proof is useless.
20 * 0 = 0
1 * 0 = 0
0 > 0
0 is therefore nonzero
false

20 * ∞ = 1 * ∞
for any a*b = c*d
a/d = c/b
therefore
20/∞ = 1/∞
reduce
20 = 1

20 * 0 = 1 * 0
for any a*b = c*d
a/d = c/b
therefore
20/0 = 1/0
reduce
20 = 1
Unfortunately, this doesn't hold up either.  Any rule breaks down at certain points.  This rule breaks down when both sides of the equation are undefined as in your example.  It can't really be used to prove this.  Of course, BlackMage's proof in this case also has some problems, because the "reduce" step is not as simple s he is making it out to be when one is dealing with infinity

see comments^

[Grimm]

Wow. You guys are going a lot more in depth with this than I had thought you would.

I think I'm just gonna keep on thinkin infinity isn't a number, and zero is, and I'll leave you all to your proofs and hypothesis.

[a civilian]

Wrong.  For any real number x, 1/(x+1) is nonzero.  Therefore the rest of this proof is useless

That is true; but also true is that for any real number x, x + 1 is finite.

False.  This inequality is only valid for positive numbers.  Zero is not a positive number.  Therefore the rest of this proof is useless.

Nor is infinity a positive number.

Unfortunately, this doesn't hold up either.  Any rule breaks down at certain points.  This rule breaks down when both sides of the equation are undefined as in your example.  It can't really be used to prove this.  Of course, BlackMage's proof in this case also has some problems, because the "reduce" step is not as simple as he is making it out to be when one is dealing with infinity

That division by zero is not undefined, but rather infinite is one of the things I have been arguing all along.  Without it as a premise I do not claim infinity to be a number.

[JHunz]

Maybe I should have said positive values.  Infinity is, by nature, positive.

[a civilian]

Maybe I should have said positive values.  Infinity is, by nature, positive.

Infinity is as positive as zero.  Exceed infinity (from the positive standpoint) and negativity results, as can be seen here:  2/2, 2/1, 2/0, 2/-1.  (I am, again, using the premise that division by zero is infinite.)

[JHunz]

Infinity is the largest value possible.  Therefore, you cannot exceed infinity by definition, nor can it be anything but positive.

[a civilian]

In a way you can, as I just did it in my example.  But regardless, infinity can be approached by either addition or subtraction, which shows that it is not positive.