Can 1 be "close" to 0?

[morgsboi]

Generally, if you ask people if 1 is a close number to zero they would say yes. But is that true? The way I see it is 0 means nothing or non-existent and 1 has a value so to me it is a leap form existent to non-existent. However, if you look at a number line for example, 0 and 1 would be right next to each other.

 

Also, I was wondering if numbers can have their own type of relativity. What I mean by this is comparisons to the size of the number (or anything really). I think this because 0.0001 could be "larger" than 100000 if it's compared to other numbers such as 0.00000000000000001. Perhaps there is a word for it so if you know it, it would help me out. Thanks

[The Observer]

Measure Theory

 

I think you are looking for something like this. Unfortunately it is a somewhat technical subject.

[morgsboi]

Measure Theory

 

I think you are looking for something like this. Unfortunately it is a somewhat technical subject.

 

Thanks, although I understand small bits of it, that defiantly does seem to complicated for me.

[ydoaPs]

Yes, 1 is close to 0. It's about 1 away from 0. See: number line.

[morgsboi]

Yes, 1 is close to 0. It's about 1 away from 0. See: number line.

 

As I mentioned in my post:

However, if you look at a number line for example, 0 and 1 would be right next to each other.

But does that actually make sense? I see them as physically close in writing but the numbers themselves are not close. In fact 0 isn't a number because it doesn't tell you how many of something exist. It tells you that it doesn't exist.

Also, see the top paragraph of my topic. Define "close".

[The Observer]

Are talking about the real numbers 0 and 1 or the integers 0 and 1?

[morgsboi]

Are talking about the real numbers 0 and 1 or the integers 0 and 1?

 

It doesn't matter, same result.

 

It doesn't matter, same result.

Edit: Apologies, not real numbers if we are talking about the markings of no significant value across a number line.

 

 

 

[DrRocket]

Generally, if you ask people if 1 is a close number to zero they would say yes. But is that true? The way I see it is 0 means nothing or non-existent and 1 has a value so to me it is a leap form existent to non-existent. However, if you look at a number line for example, 0 and 1 would be right next to each other.

 

Also, I was wondering if numbers can have their own type of relativity. What I mean by this is comparisons to the size of the number (or anything really). I think this because 0.0001 could be "larger" than 100000 if it's compared to other numbers such as 0.00000000000000001. Perhaps there is a word for it so if you know it, it would help me out. Thanks

 

 

Measure Theory

 

I think you are looking for something like this. Unfortunately it is a somewhat technical subject.

 

Measure theory is not the right theory for this question. I deals with a notion of "size" of sets, something akin to length, area, volume, etc. Measure theory is used in the general theory of integration and when specialized to positive measures of total mass 1, yields the modern theory of probability.

 

The notion of a point or number being close to another point or number is usually embodied in the topological notion of a "neighborhood". In the case of the real line or a the typical Euclildean space one has a notion of distance, a metric, that serves to define the topology and to measure "closeness" of distance of one point relative to another. So, you might look to an introductory topology book for more ideas related to your question. Maxwell Rosenlicht's Introduction to Analysis has a nice elementary treatment of metric spaces, and Lecture Notes on Elementary Topology and Geometry by Singer and Thorpe goes further and presents a very nice introduction to more general concepts of topology and geometry.

 

0 and 1 are not "right next to one another". In fact there are infinitely many numbers between then -- uncountably many in fact.

 

One might thing of "relativity of size" of numbers via the notion of ratios, but any sensible comparison would still view 100000 as being larger than 0.00001 if the two are compared using the same criteria.