Math Philosophy-- Why does 1/∞ not equal 0, and for that matter, what is ∞?

Originally posted by PhysicsAdept
reply to post by OccamAssassin

 

Here's a question I have wondered for a while... What is the purpose of other bases? I mean I know that we use decimal and it works out nicely because I am used to it, then base 2 is used for computers... probably because analogue things works off of a system similar to binary I am guessing, then there is hexadecimal. I don't know exactly the these bases are used instead of the others, but I am really curious to how the other bases benefit the world, what are the other bases even used for?

Base 60 is used for time.

Hex is used because of how computer hardware is structured. Eight bits in a byte. (four bits in a nibble for the old four bit systems from the 70's). Eight is the logical base of choice as it can be scaled up easily(a 64 bit system is still base eight).

I should add .....computers work using base 2 and base 8 together.

Think of base 2 as on/off for individual tracks/wires......eight wires/tracks make a byte. The system will operate on a base 8 architecture as far as the operating system is concerned....The computer will be operating at base 2 as far as the primary hardware is concerned.....the cpu.

reply to post by Riakennor


I will need to check that video out, and then get back to you on what I think, thanks!

reply to post by OccamAssassin


Ah yes, base 60 is time... No THAT I have never thought of, yet now it makes so much sense... Hmm. Well what if I was to have a base of some fraction? That is not possible correct? I mean I cannot think of what that would even entail but I am just wondering... When talking about something like a sign wave where the maximum value is 1, it would make sense to have some type of different numerical system to describe it....

Wow that is pretty out there. Now that time I agree I have been subjected to over-thinking

heh
use some logic and go out of pure math
0 is lack - nothing is there
1/∞ is a presence - there is still an element existing
so 0 ≠ 1/∞
and 0 < 1/∞ (which - the 2nd statemant - is quite stupid IMO since zero cant with anything xD)
∞ by itself is whole/maximum - there cant be end or anything beyond it
OTOH it can in theory (or philosophy rather xD ) end if we adapt to 'real world' or assume some absolute limit
but as an abstract it is ... well it is just an infinity xD

btw
in no border line situation
∞ = ∞+1 (and any other ∞ variation like ∞*n)
someone wrote 0 is the limit (how can nothing be a limit)



it all can seem quite a lot of absurd for those that never got deeper into math/logic/philosophy

and please excuse me for my horrible english xp

reply to post by PhysicsAdept


Hmmm, fractional bases......I hadn't thought of that.

As the number gets larger... It is actually getting smaller.

the fun begins when you go out of the box
pure math, philosophy and reality are different entities (which can and often do get along)
every approach can have a different result and different view on the topic
thats where most ppl get headache

math is just a helper and in many cases just a 'game'
does fractions really exist? the same goes to negative numbers
they are just a tool with no touch in reality but which is neccessary for math as a whole
(you can argue about fractions but the damn apple example can be used in both ways: for and against it)

most ppl minds explode
thats why I love it

reply to post by PhysicsAdept

i don't think one infinity can be larger than another. i think infinity-infinity cannot be done. it is true that there are an infinite amount of numbers between any two real numbers with different values.

we can theoretically consider infinity-infinity, but there is no answer because math is a language and in this instance it is being used to describe something that not only doesn't exist, but cannot exist.

it's back to the "unstoppable force vs. unmovable object" scenario. there is no answer because the question is a paradox. like i said in the beginning, paradoxes result when infinity is included.

reply to post by PhysicsAdept


That's right. From infinity you can't count down to zero, which means that we're already in eternity, whether you believe in the "big bang" or not, which itself could very well be one of an infinite number of singularities. This would then logically lead to the notion of an eternal recurrence, to which I would add evolutionary eternal recurrence, meaning that while the present configuration of now, is eternal, as an eternally unfolding now, it will never repeat itself, except at a higher level, once integrated. Reality itself then is an eternal evolutionary process of differentiation and reintegration, within an ever expanding sphere of perfection, wholeness and integrity. The implication is this is astounding, and signifies, at least to me in my mind and from what I've gathered, the immamence of the kingdom of heaven made present, as a higher reality, always ascending and descending, drawing forever upward that which is lowly, towards ever increasing heights of perfection, as an eternal, evolutionary, process, within with we are already included, and cannot be excluded, unless our aim and our will has been corrupted and has become already fruitless, then we're in need of yes, redemption and forgiveness, to clear the slate, and in truth, the whole thing is "rebooted" and made fresh at every moment, since the truth and the reality itself is never static, and therefore never dead. We then, to experience life and reality as it is and participate more fully, need ourselves also to be rebooted and made new again, and brought from dead, to alive in a type of baptism, in the living waters of cosmic awareness and the free flow of the living water of eternal life as it is, lived more fully and completely, in eternity.


1/∞ = heaven (or hell of one's own making).

This is very good news (with only a very small warning)!

Best Regards,

NAM

Originally posted by PhysicsAdept
One, day, I hope I do know a great deal of math. I am going to go to Colorado School of Mines and become a Physicist.

I can't wait to have a future colleague who gets excited like I do about mathematical physics.

As to the topic: Infinity can be quantified only in geometry i.e. nested sequences. It's a mathematical object for our convenience to calculate, just like a particle or 'point' in physics, it does not actually exist.

When we try to quantify it in the real number system, we run into the problem of inconsistency or incompleteness, hence the arithmetizing it as a proper quantity like 5 or 7 dismisses the entire system doing the examination.

Originally posted by PhysicsAdept
reply to post by Sly1one

 

Personally I don't think anyone understands the concept of infinity. Try putting yourself into a position. This position is one in which you have just broken the infinite plane. That you exist somewhere, that is no ∞ away from where you started, and perhaps another ∞ past that point. Where then do you exist? This is where the philosophy has to come in, not necessarily the math.

But you claim to understand it well, or at least much more than I do, so then tell me what you think.

I didn't mean to come off "know it allish" as I am not and am learning new things being humbled every day.

However a few quotes of yours contradict the concept or notion of that which is infinite...

The thing about this calculation is that in order to produce that result of 1/3... we assume we have reached infinity, have we not?

Again infinity not being a destination or a point...there is no "reaching infinity"...anytime you ascribe a point you have quantified. You can quantify a foot into infinite segments or into 4 segments 5 segments, 6 segments or 16 segments it doesn’t matter...all numbers=∞

There is no such thing as a "foot"...or a "meter" they are man made tools that are very useful and practical for us to navigate ∞ and because these are agreed upon standards of measurement...they work. This same concept works for time and the imaginary minutes within a day.

So because ∞-∞ does not =0, you would agree that some ∞s are larger than others?

∞>∞?? would imply they are not equal which implies they are finite...which is contradictory to the concept of infinity.

Even if you said ∞(a)>∞(b) may I ask what the difference is between ∞(a) and ∞(b)?? there is none thus there is no reason to separate them into an equation...∞=∞ period...

Many people have gone insane dabbling with infinity because it is a concept that warps the mind back and forth in contradiction. I think this is ultimately because when using practical math you are constantly trying to quantify and sum that which is not quantifiable.

I will use the circle again as a mental illustration:

Mathematically the "circumference" of a circle is only possible when you CREATE from thin air a point from which to start and end your measurement. It doesn’t matter where you create it so long as there is a point for you to start and finish measurement ie: quantify.

Philosophically, there are no points from which to start and finish measuring a circle, it warps around itself endlessly. This is “infinite” where the other “mathematical” circle is finite…now I ask which one is an illusion? The infinite circle? Or the finite circle? Or are they both real?

I can tell you which one is practical and useful to build a house…but other than that…im not quite sure.

Here is another example of quantifying infinity:

A man is walking to a bus stop 50 feet away, before he gets to the bus stop he must first walk half way there, and before he gets half way there, he must walk half way to half way there…so on and so forth forever…so in essence this man has traveled an infinite distance to get to the bus stop.

The points between A and B, start and finish are infinite…yet we can travel between the infinite points of A and B…
The best example that I can possibly think of that is both infinite and finite is circle, its both infinite and finite depending on how you want to look at it. Make it 3d and it becomes a sphere. If the universe is indeed finite, I would imagine it being like a mobius trip sooo large we could never perceive it and thus would walk around in circles infinitely. The curvature of space could be so slight that we would never perceive it wrapping around on itself. Much like how we used to perceive the earth as flat or liner and we would wander “how far out it goes” when we only need to wonder “how far around it goes”.

The reason why the math werld thinks .9 to infinity equals 1 is because they've assigned the Space-Time of Numbers to inbetween the numbers instead of the number itself. Once they correct that error, then Zero will occupy Space-Time and the only Space-Time it can possibly occupy is finite and finite is the reason why 1/∞ not equal 0, for 1/∞ equals finite.

Ribbit

reply to post by PhysicsAdept


Let's look at two things, Infinity and Limits.

First let's look at the Limit function. When you take the limit of a function...you really shoudn't say the equation at the upper bound of the limit function equals the answer. You use the limit function to find the boundries of another function.

For the Limit of 1/x as x approaches infinity, the answer should really be read as "it approaches zero" and not as "it equals zero".

I think this may be were some of the confusion comes into play. You see an "=" sign and you think 1/infinit EQUALS zero. But you should really think of it as "The limit of 1/x as x aproaches infinity is zero"...meaning it is bound by zero...it will never reach it...it will never cross it.

Let's look at another example. The limit of ( sin x ) / x as x approaches 0 is 1. But I know you would never claim that ( sin 0 ) / 0 equals 1...because you know you can't divide by zero.

We use limits to find the boundry of the function...not to find the answer at the end limit.



Now for infinity. It isn't a quantity, it isn't a number...it is a description of the boundry. It is using a concept to describe a boundless set. You can't use it as a number any more than you can use the concept of "large" or "small" as a number. What is 2 * large?

For your question about 1/infinity. Let's try a different approach.

If you think 1/infinity equals zero because of the limit function. Then you also believe that 10/infinity equals zero...because the limit of 10/infinit is also zero. This introduces a pradox for you.

1/infinity = 0

10/infinity = 0

1/infinit = 10/infinity

1 = 10

And it doesn't stop there...if what you want to say x/infinity = 0 for any number...then you are esentially saying that x = y for all real numbers where x and y are different numbers.



I hope this makes sense...I want to explain a lot more...but I'm heading out to dinner...I'll be back later though because I do love math.

Originally posted by PhysicsAdept
reply to post by OccamAssassin

 

Ah I see now, does .9 repeating=1? Yeah I wonder that too... I read an article once and for the life of me I cannot find it... I figured it would make what I say to be more credible, so if anyone can find it they should post a link. I read once that because of limits, .9r actually does equal 1, at least in all practical senses. Does this mean mathematically we can call it 1? Probably not... because then 1 would equal 1.0r1, then that would end up reaching 2 at some point, basically stating that 1=∞, or ∞=∞ like someone else in this post has said...

.9 repeating actually doesn't equal one. It's a perfect example of how math doesn't equate EXACTLY with reality. Once again, man trying to "contain" the infinite.

Using infinity as if it was an integer in any math is an invalid application. Infinite is both all operations (kinetic, current) and all existences (static, voltage) at the same time.

Originally posted by tkwasny
Using infinity as if it was an integer in any math is an invalid application. Infinite is both all operations (kinetic, current) and all existences (static, voltage) at the same time.

What do you mean? Is Pi not an infinite decimal number? Is 1/3 not .333 repeating for infinity?

It's because as hard as it tries, Math just can't express reality perfectly.

reply to post by graphuto


Example:

I cut a pie into three pieces. I have 3 pieces of a whole pie. Math tells me that there is only now .9999 repeating left of that pie, but observation tells me that the whole thing is still there.

numbers represent things. 0 represents nothing.

infinity is every number greater and less, starting from 0 and running forever.

since time plays a factor, it is physically impossible to divide or multiply something than never stops going.

every second the numbers change.

so you'll never know the correct answer because if you stop infinity to multiply it, it is no longer infinity.

but if the known universe will come to an end one day. then infinity doesn't exist.

so at the end, 0 is infinity. since nothing doesn't have an end because it doesn't exist.

Originally posted by graphuto
reply to post by graphuto

 

Example:

I cut a pie into three pieces. I have 3 pieces of a whole pie. Math tells me that there is only now .9999 repeating left of that pie, but observation tells me that the whole thing is still there.

No, math does not leave .9999r left of that pie. Math tells you that you have 3 pieces of the pie, all 1/3 of the original. If we try to write 1/3 in decimal form, it is 0.3r of the original. If anything, math would tell you that you have 0.0r1 left over of the pie...which isn't even correct notation because no one ever uses it...but it would be 0.0(repeating infinitely)1.

It's an issue of our numbering system. If we would use base 3....than 1/3 (base 10) would be 1/10 (base 3)...which equals 0.1 (base 3).

Originally posted by PhysicsAdept
reply to post by OccamAssassin

 

Here's a question I have wondered for a while... What is the purpose of other bases? I mean I know that we use decimal and it works out nicely because I am used to it, then base 2 is used for computers... probably because analogue things works off of a system similar to binary I am guessing, then there is hexadecimal. I don't know exactly the these bases are used instead of the others, but I am really curious to how the other bases benefit the world, what are the other bases even used for?

There is no "purpose" for any other base...they just exist.

The most accepted argument as to why we use base 10 is because we have 10 fingers. Computers use base 2 because the digits are 0 and 1 and we can create hardware that represent a 0 or 1 using different voltages. Base 16, Hexadecimal, is used because it is easy to convert from hex to binary and it is easier to work in hex than it is in binary.

Someone else said time uses base 60...but that isn't entirely true. I'll respond to that post to explain why.

reply to post by OccamAssassin

Base 60 is used for time.

Time really doesn't use base 60.

I see where you are thinking that...but it doesn't use base 60.

In a base 60 system...if you were counting seconds there would no "10" after "9"....there would be some other symbol like "A". "10" in base 60 is "60" in base 10.