John J. Bannan
Registered Senior Member
:shrug:
Does 0+0=0?
- Thread starter John J. Bannan
- Start date
:shrug:
John J. Bannan
Registered Senior Member
How do you know its an open problem among mathematicians? Are you a mathematician?
Enmos
Valued Senior Member
What you mean the character, or what it represents ?
Zero has NO size and NO value, It's simply a convenient construct, a concept, not something that has physical nor mathematical attributes.
John J. Bannan
Registered Senior Member
What it represents.
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John J. Bannan
Registered Senior Member
If zero has no size, then how can you add two of them together?
John J. Bannan
Registered Senior Member
Is an infinitely small number equal to zero? If an infinitely small number has size and is also equal to zero, wouldn't that mean zero has size?
John J. Bannan
Registered Senior Member
I disagree. If you take an infinitely small number, as close to zero as possible, the infinitely small number still has size. If you equate zero with an infinitely small number, than zero has size. Moreover, you could add two infinitely small numbers together, and the result would be the same thing, an infinitely small number. Remember, infinity plus infinity is still infinity. Therefore, it is consistent to say 0+0=0. But, it is also plain that zero has size, although infinitely small.
Interestingly, this means that absolute zero cannot exist, because you can always find a smaller number that comes closer and closer to absolute zero, but infinitity prevents you from ever reaching absolute zero. In other words, zero is the end of the line for infinitly smaller numbers. Since infinity does not permit the end of the line, absolute zero cannot exist. Therefore, the "0" of mathematics is really just an infinitely small number - which must have size. Either that, or infinity can't exist - which seems doubtful in light of the fact that I can always add more zeros to .000000000000 et cetera
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John J. Bannan
Registered Senior Member
Well, BenTheMan closed my thread asking the question whether an infinitely small number is equal to zero - to which he answered yes. Accordingly, there seems to be agreement that zero has size. This means nothingness, as analogized to zero, has size. And if nothingness has size, then there can be multiple nothingnesses, as size implies others can share that size.
Humor that zero is a real number, then there are actually real processes it plays, and we know this by simple $$n->(0,1,2... ,10)$$, as John was saying, we still use zero, but can we reflect on the zero as it swaps its place when in a positive time direction like above? We can, i think... but we need to see the values of zero as something completely new, and possibly exciting.
$$0*+0*=0''$$
then $$0'-0'=0**$$
then what would $$0**+0'' = \pm 1$$
But that is only if $$(0-0)(0*0*)=1$$
If we restrict a complex structure like the universe to a time where there was nothing, space and energy also need zero values. But there is absolutely no reason there can be no corrolation to giving a time before [zero], unless zero marks a point which operates like the superpositining found in physics as 0.50 and 0.50, when upon a collapse, yields either $$\sqrt{1}~or~\sqrt{-1}$$, because as i explained, you can have an increasing value of $$i^2$$ and expect $$i^0$$ to be invalid, when we use the imaginary terms in also real values $$\sqrt{-1}$$.
$$0*+0*=0''$$
then $$0'-0'=0**$$
then what would $$0**+0'' = \pm 1$$
But that is only if $$(0-0)(0*0*)=1$$
If we restrict a complex structure like the universe to a time where there was nothing, space and energy also need zero values. But there is absolutely no reason there can be no corrolation to giving a time before [zero], unless zero marks a point which operates like the superpositining found in physics as 0.50 and 0.50, when upon a collapse, yields either $$\sqrt{1}~or~\sqrt{-1}$$, because as i explained, you can have an increasing value of $$i^2$$ and expect $$i^0$$ to be invalid, when we use the imaginary terms in also real values $$\sqrt{-1}$$.
0 is a concept meaning 'no quantity'. When you add 0's together:
-> 0 + 0 = 0
then it reads as:
-> no quantity added to no quantity equals no quantity
In other words it is a redundancy.
Yes. That's where it came from in the first place.
No. It is an arithmetical identity that x + 0 = x for all x.
The concept of the "size" of a number is meaningless. Only physical objects have size.
As close to zero as possible is zero.
Remember, you said "infinitely small". That word "infinite" will get you into all sorts of trouble.
No. That would imply that zero is an object.
The fact that a number is a limit of some process doesn't mean the number itself doesn't exist.
For example consider the limit of the series:
1 + 1/2 + 1/4 + 1/8 + ...
This sum has an infinite number of terms. The limit of the sum is 2, but no matter how many terms you add up (unless it is infinite), you'll never reach 2. Does that mean 2 doesn't exist? Of course not.
What's the matter, didn't you understand the mathematical definition of zero I gave in your other thread?
lol thanks James R, finally someone added an intelligent response.
To the original poster, the fact is that zero is a mysterious concept, similar to infinity.
many equations and formulas give a definition of zero. The two most impressive are the limits of 1/n and Euler's equation.
First is the relationship between infinity and zero.
$$\lim_{n \rightarrow \infty } {1 \over n} = 0$$
$$\lim_{n \rightarrow 0} {1 \over n} = \infty $$
The relationship is clearly expressed in your argument. $$0+0=0$$ and $$\infty + \infty = \infty$$
Another equation equal to zero is so impressive that Feynman called it our crown jewel.
$$e^{\pi i} + 1 = 0 $$
To the original poster, the fact is that zero is a mysterious concept, similar to infinity.
many equations and formulas give a definition of zero. The two most impressive are the limits of 1/n and Euler's equation.
First is the relationship between infinity and zero.
$$\lim_{n \rightarrow \infty } {1 \over n} = 0$$
$$\lim_{n \rightarrow 0} {1 \over n} = \infty $$
The relationship is clearly expressed in your argument. $$0+0=0$$ and $$\infty + \infty = \infty$$
Another equation equal to zero is so impressive that Feynman called it our crown jewel.
$$e^{\pi i} + 1 = 0 $$
Enmos
Valued Senior Member
In that case no. What size does something with zero volume have ?
It has no size.
You don't. That's the whole point. 0+x means "add nothing to x"..
Enmos
Valued Senior Member
No, an infinitely small number approaches zero, but it is not equal to zero.