Conway,
The part of my post that was directed specifically at your statements was
So yes I am aware who introduced the idea of near infinity and yes I was suggesting to Archie that this idea may have some (or even much) merit.Before you can say what infinity is or is not or 'near infinity' or approaches infinity means you have to have a working definition of infinity that provides properties we can compare with.
Your response proves without doubt that you are not prepared to engage, you simply lash out those around you, even those who have just agreed with you.
You not only introduced the idea of near infinity you also introduced just plain infinity and I asked to you provide your definition for discussion.
Archie
I concede to you the point on the difference between numbers and a numerals. Nor where you nit picking. I now find valid truth in you point here. So then I shall say I am only referring to numbers not numerals, as possessing space and value. So then if you could make a fresh assault as to why numbers (do not/ should not) posses both value and space inherent in the symbol itself.
Studiot
If you do not post an equation I will cease to reply to you. I have found that between you and I, equations are the only language that will exchange information between us. If you need starting point.
0*a = 0*a + 0 = 0*a + (0*a + -(0*a)) = (0*a + 0*a) + -(0*a) = ((0 + 0)*a) + -(0*a) = 0*a + -(0*a) = 0.
or
0(s) * a(v) = 0(s) * a(v) + 0 = (0(s) * a(v)) + -((0(s) * a(v)) = (0(s) * a(v)) + (0(s) * a(v)) + -(0(s) * a(v)) = ((0+0)s * a(v)) + - (0(v) * a(s)) = 0(s) * a(v) + - (0(v) * a(s)) = a
you will note both equations are the exact same.
I would love to express my true opinion on this post but as I have already been banned from two so-called "intellectual" (ptthshhshshsttttt) websites this past month, I dare not risk getting barred from this one as well for fear of causing a quantum rip in reality. So consequently I will refrain from telling the poster exactly what form of unicellular life I consider him to be the intellectual equal of.
I made a mistake in the third equation
(0(s) * a(v)) + -((0(s) * a(v)) = 0
here....
(0(s) * a(v)) + - ((0(v) * a(s)) = a
As to your equation. What does T1 and T2 equal? Given this I may solve. Also what is meant by efficiency?
Matt..."No matter how fast or how far you run, you're still in the space where you are." -- Russell
All things then contain space. Including zero.
t1 = 0
( t2 - 0 )v / 0s = t2
t2 = 0
( 0 - t1 )v / 0s = t1
To be fair, it is only * by 0 that is relative. That is in / by zero, value is labeled first and space is labeled second.
This is the equation that powered the industrial revolution and one of the most famous equations in history.As to your equation. What does T1 and T2 equal? Given this I may solve. Also what is meant by efficiency?
Are you saying you don't understand it?
It is the expression of the efficiency of an ideal heat engine.
Now I asked you pleasantly for your definition of infinity and you were confrontational in the extreme in your reply, demanding an equation.
Why are you now asking for my definition of the terms in an equation?
However I will comply.
T_{2} and T_{1} are the temperatures of the hot and cold reservoirs respectively.
Efficiency has its usual definition.
I posted this equation because it contains two infinities and uses the properties of such infinities that I mentioned previously, but does not involve a real or imagined division by zero.
I could equally have chosen many other equations from the applications list I gave before or beyond.
I was not aware of this information thank you. If then, as stated by you...
"but does not involve a real or imagined division by zero."
then what does the equation have to do with this idea. If both t1 and t2 are infinites, finites, or anything other than zero, than the sum is not affected or changed by this idea at all.
I didn't say that T_{1} or T_{2} were infinities.
I said that the equation contained two infinities.
Furthermore T_{1} can be 0 in theory but T_{2} cannot. This is why division by zero is not an issue.
If you don't follow something you should ask for clarification, not guess and certainly not jump to conclusions that do not follow.
I also said that the use of the infinities involved the most basic property of infinity, a property far more basic than division of any kind.
You still have not provided your definition of infinity.
One easy argument is that numbers are dimensionless, space is not.
Another is that numbers are abstract and thus do not have any physical existence in space. This is more of an argument to say that your specification of space is pointless because it is the same for all numbers and therefore adds nothing to the number system. I could say that all numbers are purple but it wouldn't make them operate any differently. The interest would come if we also had some red numbers that interacted with the purple ones in a different fashion to which purples interacted with purples.
Studiot
I clearly asked you what t1 and t2 where. Thus I asked for clarification. It would have been just as easy to look up the meaning of the equation, thus never show a gap in my knowledge, being as this is the internet. So clearly I had no intention of "guessing" at something I didn't know. Further I have already offered and solved the equations for t1 being zero. Again if t2 is not zero, not a point. Additionally I have already provided a definition for infinity. If you do not remember please ask instead of jumping to conclusions.
Archie.
Prove to me that a number is dimensionless. I know that I can measure a number, therefore it seems to have a dimension. It seems to me only your opinion that numbers have no dimension. Likewise it is only my opinion that they do. Again I am of the opinion that abstraction posses a length of space. It is only that it is to small for us to define. If then zero has a measure of space, and that amount of space varies, and if all numbers have space and these length's vary, then essentially we do have "purple" numbers interacting differently with "red" numbers.
Yes indeed you did, and quite reasonably at that.I clearly asked you what t1 and t2 where. Thus I asked for clarification.
And equally reasonably I answered you.As to your equation. What does T1 and T2 equal? Given this I may solve. Also what is meant by efficiency?
To which answer you jumped to the following conclusionT2 and T1 are the temperatures of the hot and cold reservoirs respectively.
Efficiency has its usual definition.
I posted this equation because it contains two infinities and uses the properties of such infinities that I mentioned previously, but does not involve a real or imagined division by zero.
Having just been told that T_{1} and T_{2} are temperatures, were you seriously expecting to discuss infinite temperatures?If both t1 and t2 are infinites, finites, or anything other than zero, than the sum is not affected or changed by this idea at all.
I also told you that
and thatI didn't say that T1 or T2 were infinities.
I said that the equation contained two infinities.
So I am suprised you chose not to ask more about this, but returned to a personal confrontational.I also said that the use of the infinities involved the most basic property of infinity, a property far more basic than division of any kind.
I had intended to expand on this very point about infinities, but that in order to have a fruitful discussion about infinity we need to have a working definition of the word or concept and agree on the (important) properties.
That is why I have repeatedly asked for your definition so that I can swop with mine and compare.
As far as I am concerned, infinity has the fundamental property that if you add any finite number (or quantity) to it, or subtract any finite number (quantity) from it the infinity does not change.
Division does not even need to be defined, let alone considered.
This idea has vast implications and use in applied maths as have already said.
Let me pose a few examples
What is the property of a cold/hot reservoir that makes it so?
What is the property of an electrical earth that makes it an electrical earth?
What does infinite dilution mean in chemistry?
If you inflate a balloon in the atmosphere, how does that affect does the volume and pressure of the atmosphere?
As a matter of interest Carnot's equation, that I gave, can very well be used to discuss the dimensional aspects of numbers you are currently confronting Archie about.You still have not provided your definition of infinity.
Finally to try to move this discussion forwards do you understand the terms extrinsic and intrinsic properties?
This has definite implications for you "number and volume" theory.
I have provide a definition for infinite. Pleas re-read the original post. I await with all respect. Thank you for your time and continued interest. An extrinsic property is a property held from outside of the thing itself. An intrinsic property is a property held from within the thing itself. I am surprised you missed the mathematical mistake in my first set of equations. I ponder is you just skimmed them? I respect you, I wish this conversation to continue. I will try to learn from you and to be patient. But we must dispense with any further negative comments....agreed? Personal or academic.