Enmos
Valued Senior Member
Ben was wrong.
Does 0+0=0?
- Thread starter John J. Bannan
- Start date
Ben was wrong.
I don't know. Ben was looking at the initial point being "An Infinitely small number" as I gather you know (but I'm stating for those to clarify it it), Infinity has no end in the sense that it's a loop, in this case an ever decreasing number. Although the value can be considered greater than zero (nothing) for the most part any mathematics wouldn't deal with it as a whole number because of rounding, and rounding Rounds down if something is less than .5 to the nearest 'whole' number.
(Technically this proves zero to be a Whole number because when you round 0.4 to a "whole number" you are left with "0")
Enmos
Valued Senior Member
Yes, but since infinity has no end an infinitely small number never actually reaches zero.
An infinitely small number thus approaches zero but never reaches it.
Of course, people treat it as being zero for practicality reasons.
Now I wish I could use this tex..
Edit: I copied something from Camilus that makes my point.
$$\lim_{n \rightarrow \infty } {1 \over n} = 0$$
n approaches, but never reaches, zero.
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Enmos
Valued Senior Member
I probably wouldn't know what they were talking about..
John J. Bannan
Registered Senior Member
Numbers are infinite. Nevertheless, we still say 1 exists. You can imagine an infinitesimally small fraction less than one - and seemingly you should never reach 1. And yet, we reach 1. This is similar to Zeno's paradox. The fact that there are an infinite number of fractions of 1 - does not mean 1 does not exist. But, we are still dealing with infinities here. So, although 1 exists, infinities suggest 1 has no size. The second you give 1 a size, then there would be a finite number of fractions between 1 and zero - which is mathematically incorrect as there are an infinite number of fractions between 1 and zero. But, paradoxically, 1 does have size - doesn't it? It has relative size. 1 is half the size of 2. Therefore, zero has relative size as well. As far as infinities go, zero is no different than 1. They both confront the same problem with infinities as analogized to Zeno's paradox. You can imagine an infinitely small number ever approaching zero. But, how do we actually get to zero? Well, zero has as much right to claim to exist as 1 has a right to claim to exist. Therefore, if 1 exits, then zero exists. But, zero has a relative size, just as 1 has a relative size.
The interesting problem is what happens when you add zero and zero together. Both zeros have a relative size to each other, so now you have 2 zeros instead of just one. This is why you can add two zeros together - due to their relative size to each other. And yet, two zeros still add up to only one zero. How is this possible? If you think of zero as an infinitesimally small number, and you add two infinitesimally small numbers together, you still get an infinitesimally small number. So, the equation 0+0=0 is consistent - but it also allows for a relative size for zero to itself. This is my explanation as to how something can come from nothing. The relative size of zero to itself repeated infinitely creates the relative size of other numbers. Adding together an infinite amount of infinitely small numbers cancels out the infinities and creates real numbers. An infinite amount of zeros can come from a single zero, as 0=0+0+0+0+0+0 et cetera.
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John J. Bannan
Registered Senior Member
Didn't you just agree in another thread that an infinitely small number is equal to zero? But, an infinitely small number must have size, because it is a number infinitely shy of zero. So, then zero would have size, if you equate the two.
Wait a minute, weren't they the ones who stole von Strudel's early work before he had time top publish ?
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John J. Bannan
Registered Senior Member
Here's a question for you Myles. What is the first fractional number past zero heading toward 1? Some posters have claimed (and perhaps, rightly so), that the infinitesmially small number is equal to zero. We'll, if that's true, then what is the smallest number not equal to zero?
These same posters also are claiming that zero has no size. But, does 1 have size? If 1 is half of 2, then doesn't 1 have relative size?
No, an infinitesimally small number is a number whose absolute value is less than any positive number. Zero is the only such number.
John Bannan:
No, they aren't.
It's not clear to me in what sense you are using the term "size" now. It sounds like you're thinking of numbers as intervals, as if the number 1, for example, "stretched" from 0.999 to 1.111 or something. Think of a number line. Are you saying that individual numbers on the line take up some fraction of the line? If so, then that is wrong. Numbers are points on the line. The number 1 has no extension - it is a point of zero width on the number line.
Does that help?
Addition is not defined with reference to "sizes". As I said before, it is an arithmetical identity that x + 0 = x for all x. Therefore 0 + 0 = 0.
Here's another identity: 0x = 0 for all x except x=0. Therefore 2 times zero is zero, for example. So, 2 zeros is the same as 1 zero - it has the value zero.
Zero isn't an infinitesimally small number. It is zero. Thinking of it as an infinitesimally small number is giving it "size" which it does not have.
No, they aren't.
It's not clear to me in what sense you are using the term "size" now. It sounds like you're thinking of numbers as intervals, as if the number 1, for example, "stretched" from 0.999 to 1.111 or something. Think of a number line. Are you saying that individual numbers on the line take up some fraction of the line? If so, then that is wrong. Numbers are points on the line. The number 1 has no extension - it is a point of zero width on the number line.
Does that help?
Addition is not defined with reference to "sizes". As I said before, it is an arithmetical identity that x + 0 = x for all x. Therefore 0 + 0 = 0.
Here's another identity: 0x = 0 for all x except x=0. Therefore 2 times zero is zero, for example. So, 2 zeros is the same as 1 zero - it has the value zero.
Zero isn't an infinitesimally small number. It is zero. Thinking of it as an infinitesimally small number is giving it "size" which it does not have.
''Zero isn't an infinitesimally small number. It is zero. Thinking of it as an infinitesimally small number is giving it "size" which it does not have.''
$$1=(0.50i)(0.50i)= \sqrt{-1}$$
Here, 0.50 can be considered a value under 1, and yet also considered as not actually being real at all. So in a sense, this superposition is a proof that zero has some kind of value with another conjugate.
$$1=(0.50i)(0.50i)= \sqrt{-1}$$
Here, 0.50 can be considered a value under 1, and yet also considered as not actually being real at all. So in a sense, this superposition is a proof that zero has some kind of value with another conjugate.
No, you look again. 0.50 is in this sense, a value that is undefined, much like how $$i^0$$ is JUST accepted to have an undefined value. It's only when something is added to this $$i$$, as an increasing variable, can we have the logic that $$i^0$$ must have some authority when added with a conjugate.
So, the conjugate of $$i^0$$ in this sense, is just another 0.50, so when you add the two together, oh (I apologize, i never had a plus sign, but never mind that, because you can still square two imaginary signs to produce a real number, which relevates into $$\sqrt{-1}$$, with the proof of complex-numbers.
So, the conjugate of $$i^0$$ in this sense, is just another 0.50, so when you add the two together, oh (I apologize, i never had a plus sign, but never mind that, because you can still square two imaginary signs to produce a real number, which relevates into $$\sqrt{-1}$$, with the proof of complex-numbers.