Unfortunately, we aren't talking about stars having an infinite distance. We do not know if the universe is infinite or finite so I am not really sure why you think that current physics understanding is correct..
Well we are? The whole point of the paradox is assuming that if the universe is infinite a contradiction can be derived. But if the assumption causes the contradiction to be invalid then so is the paradox.
Furthermore current physics understanding is the best understanding we have; otherwise it wouldn't be our current understanding, and the understanding I was referring to was of the thermodynamics quoted.
Let's all try to share abit of knowledge so that we can all grow. What is your favourite paradox? it can be anything from maths to physics to philosophy itself.
Also please try to give a very brief explanation of the paradox if you understand it.
Fair enough, maybe the real life analogy was not such a good idea. Still though, no matter how many 9's you have past the decimal point, there will be one more 01 if subtracted from 1. . .I think
I know what you mean, it's tough to get your head around. I'll see if I can explain it a little better, we'll call the number of 9s n and d the difference
n = 1 => d = 0.1 = (1/10)^1 n = 2 => d = 0.01 = (1/10)^2 n = 3 => d = 0.001 = (1/10)^3
etc.....
so if we have an infinite number of 9s, which is what recurring means (and that's the most important thing to remember, it doesn't mean a lot, it means an infinite amount) then we have
d = (1/10)^infinity = 0
Mathematicians would probably get a bit angry with me writing that, should really have used limit notation but I'm not sure what your mathematical background is.
So yeah, is d = 0 then 0.9999..... (with an infinite number of 9s) = 1
I don't really think I've helped by saying 0000...1 because it causes to think of it incorrectly; you shouldn't think of it as simply 'adding 9s on' infinite times.
0.9 recurring as a definition = 1
To deny its complete certainty you would also be denying that 0.1 recurring = 1/9 or that 0.3 recurring is 1/3
Ok, you're obviously either trolling or an idiot, be quiet
I know what you mean, it's tough to get your head around. I'll see if I can explain it a little better, we'll call the number of 9s n and d the difference
n = 1 => d = 0.1 = (1/10)^1 n = 2 => d = 0.01 = (1/10)^2 n = 3 => d = 0.001 = (1/10)^3
etc.....
so if we have an infinite number of 9s, which is what recurring means (and that's the most important thing to remember, it doesn't mean a lot, it means an infinite amount) then we have
d = (1/10)^infinity = 0
Mathematicians would probably get a bit angry with me writing that, should really have used limit notation but I'm not sure what your mathematical background is.
So yeah, is d = 0 then 0.9999..... (with an infinite number of 9s) = 1
The video was presented by an assistant professor of Physics & Astronomy in 2010, need more clues?
I know what you mean, it's tough to get your head around. I'll see if I can explain it a little better, we'll call the number of 9s n and d the difference
n = 1 => d = 0.1 = (1/10)^1 n = 2 => d = 0.01 = (1/10)^2 n = 3 => d = 0.001 = (1/10)^3
etc.....
so if we have an infinite number of 9s, which is what recurring means (and that's the most important thing to remember, it doesn't mean a lot, it means an infinite amount) then we have
d = (1/10)^infinity = 0
Mathematicians would probably get a bit angry with me writing that, should really have used limit notation but I'm not sure what your mathematical background is.
So yeah, is d = 0 then 0.9999..... (with an infinite number of 9s) = 1
Did A level but your explanation is pretty clear. It does makes sense. It's not be a paradox then it seems.
I don't really think I've helped by saying 0000...1 because it causes to think of it incorrectly; you shouldn't think of it as simply 'adding 9s on' infinite times.
0.9 recurring as a definition = 1
To deny its complete certainty you would also be denying that 0.1 recurring = 1/9 or that 0.3 recurring is 1/3
There are various explanations - one example:
let x = 0.9 recurring then 10x = 9.9 recurring
then 9x = 10x - x = 9
so x = 1
This is the way I learnt it at college, but thought it must be a paradox, however the way Mr Ben explained it makes sense now.
Did A level but your explanation is pretty clear. It does makes sense. It's not be a paradox then it seems.
Glad it was fairly clear infinities are some of my favorite things to play around with in maths, they can be sooooo beautiful a times. I'm not usually too good at explaining things though, so I'm glad I managed this time.
(2) Yeah, that one does work... I thought it was if i was crossing a road, and i crossed halfway, and then half the distance i just crossed, again etc..., would i ever reach the other side...?
Everyone must know about the grandfather paradox. I love that one!
It's like this: Just say you could go back in time and kill your grandfather (also works perfectly well for father too actually). If your grandfather dies, then obv you werent born.....MEANING you couldn't have gone back in time to kill your grandfather, MEANING your grandfather actually isnt dead, MEANING you do exist and can go back in time to kill him....and so on!
Is 2 really a paradox? It has an answer: you will never reach the destination...
Surely it depends on what the destination. If your crossing the road with a finite distance then, it will take a long long while but you would eventually get there wouldn't you?
(2) Yeah, that one does work... I thought it was if i was crossing a road, and i crossed halfway, and then half the distance i just crossed, again etc..., would i ever reach the other side...?
(2) Yes, you would. But you might get run over before reaching the other side
(2) Yes, you would. But you might get run over before reaching the other side
Hahaha! And, no you wouldn't. Because if you kept going half the distance you previously went and the first distance across the road you went was halfway or less then you would never make it to the other side, you would always be (1/2)^n times the width of the road, away from the side. (Where n is the number of steps)