Just out of interest what is the gamma factor when v = 0.999…?
Significant digits…a physics measurement concept, please review it
I can generate as many digits as I want or need, using precisely the same algorithm I’d use for calculating the square root of .7528799…
That’s an interesting question, but it seems GIGO for the Lorentz equation because
there IS NO SUCH thing as a velocity measured with infinite precision. Likewise
putting .444… in for v would be GIGO.
You can only generate as many as make sense if you want to do it right.
Significant digits outlines the rules for doing that, please review it.
A yardstick is not an electron microscope however much you might like it to be.
Very well. I cut off the calculation for the square root of .75288 at 6 decimal points, and get the same answer I’d get by cutting off the calculation of the square of .7528799… at six decimal points.
Nope, there is no way to know where to “cut off” the calculation when you are
given an infinite precision value for a physics calculation because the mathematicians said it was infinite precision, so it has to be calculated out to infinity to get the corresponding (nonexistent physically) infinite precision result, you are trying to
derive a process for resolving the erroneous introduction of the concept of infinite precision in measurement into the Lorentz equation.
Ah. I see what you mean. Just like when trying to find the length of the diagonal of a 1 foot by 1 foot square, you can’t assume that 1 is really 1.0…
Notice that even after you somehow calculate the square root, you are going to be dividing
something into .999…, which again is an infinite iterative process. The integer 1 is the fundamental representation of interval for the reals…that is why the distinction is so important when it comes to measurements
There is no such thing as 1.000… x 1.000… square in the real world that we can identify.
Well, gotta be careful here because Stanley Kubrick might of said otherwise 
“I can generate as many digits as I want or need, using precisely the same algorithm I’d use for calculating the square root of .7528799…”
Last comment on this.
No you cannot sir.
You cannot generate an infinite number. I would encourage you to think about that as it is very important conceptually (among other things)
Try the calculation and you will see that at no point do you need an infinitely long number for this calculation. You just need the next few digits, 00 for one case and 99 for the other.
Once again I must ask, 3 x 0.333… is equal to 1 if and only if 0.999… = 1. How is it you actually using the very thing you are trying to disprove?
“recursive iteration” Post # 1601 … that’s a paradox, either something is recursive OR it is iterative … please explain yourself.
You’re right. .999… is meaningless. Let’s do the Lorentz calculation properly, for an object moving at 250,000,000 m/s.
The formula says we will have to take the square root of 1 - 62500000000000000/89875517873681764, which is to say, sqrt[1 - .69540628…], which is to say, sqrt[.30459371…].
Can we do this?
You will always look foolish using words you do not understand in ways that make no sense and have already been pointed out to you as flat wrong. This isn’t even good as poetry, but it works far better as a poem than as a description of math.
5mins30seconds
It’s not terribly important if you (or the author of the video (I suspect that is you, or possibly 7777777, or possibly both)) see it as a paradox or not – what is important is that if you accept the given arguments (that 1/2 + 1/4 + 1/8 +… = 1) then you have to accept that the same arguments apply to the series 0.9 +0.09 + 0.009 + …
Im going to have to take a break here but I will eventually address all of these since so many people here have been kind enough to point out my errors.
1 - 62500000000000000/89875517873681764 = 1 - .69540628… = .30459371…
This is erroneous
62500000000000000 is a finite precision measurement…yet you are expressing the
ratio as infinite precision. If you like consider 62500000000000000.1234 which would be
more of a real world measurement. Four decimal places, and thus a ratio of 4 decimal places.
So yes you could take the square root and keep 4 digits and you would be done.
(emphasis added)
I’m not sure I understand what you’re getting at but still must ask:
Can we conceive of a circle? A ‘perfect’ circle? I ask because neither exists in “the finite real world”. And, whether they do or don’t, it has no effect on how we do geometry or on the ‘rules’ we use to study it (or perhaps you disagree?).
Don’t forget about 3 x 0.333… is equal to 1 if and only if 0.999… = 1. That step in your proof is in error.
I have no idea what you are trying to say here and will have to stop and review your posts later.
Zeno’s paradox…is a paradox in the sense that it is a concept that does not match up with our real world experience. It essentially prevents motion conceptually.
We know we can move, so it is clearly not in sync with reality.
I have no clue what you are saying but I will address it later.