If 1/3 x 3 = 1....
Why is it that 3 x 0.333333.. will never be equal to 1 no matter how many decimal places you use?
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because it is what it is0
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0.9 occurring is defined as 1.
It's one of Zeno's paradoxes.3 -
To make life easier2
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don't worry your pretty little head over it.0
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x = 0.99999999...
0.99999999... x 10 = 9.99999999...
therefore 10x = 9.99999999...
10x - x = 9x
9.99999999.... - 0.99999999.... = 9
therefore 9x = 9 and x=1
so 0.99999999... = 16 -
That seems like a flawless answer. I will have to ponder over it tonight when I have time.Callumcafc said:x = 0.99999999...
0.99999999... x 10 = 9.99999999...
therefore 10x = 9.99999999...
10x - x = 9x
9.99999999.... - 0.99999999.... = 9
therefore 9x = 9 and x=1
so 0.99999999... = 10 -
Is this charltonlife?0
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Why is it that when you take something by ship it's called a cargo
When you take something by car it's called a shipment7 -
Obviously infinity is never reached
Absolute zero doesn't exist either, just approximations to it which are called 0
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If it aint oo or o now it's 0.000000 what the feck do you lot do during your down time , there must be things more interesting to do1
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Train spotting?nth london addick said:If it aint oo or o now it's 0.000000 what the feck do you lot do during your down time , there must be things more interesting to do
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When someone asks you to justify something mathematical, just say 'bidmas' then walk away.1
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I'm a body double for Stephen Hawkingnth london addick said:If it aint oo or o now it's 0.000000 what the feck do you lot do during your down time
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I am one for buster blood vessel0
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It is purely an idiosyncrasy of the decimal or base 10 system we use. 0.333... is simply a decimal representation of the expression "a third of one whole" and is meaningless without understanding that this is what it means.
If we use Base 12, then 0.333... is expressed simply as 0.4, therefore 0.4*2 is 0.8 and 0.4*3 is 1.
We likely use Base 10 as standard because we have 10 digits across both hands, so if we were born with 5 fingers and 1 thumb (or if Norfolk was the birthplace of mathematics) then we would probably be using Base 12 as standard and we would not have this conundrum (although there would likely be a similar conundrum if we used Base 12 instead).2 -
How about Rezas average performances on the player rating threads?PL54 said:Obviously infinity is never reached
Absolute zero doesn't exist either, just approximations to it which are called 0
Surely that was absolutely zero?3 -
What about Graham's number? I started watching an Horizon programme on bbc 4 the other day about the number infinity. It mentioned google plexi and the fact that google plex was the highest number you can get but then this Graham's number (the actual number he doesn't know how to represent in digits, he does know that it ends in 7 I think), is all about the depth and dimension of a cube. If I was following the programme correctly.
Basically when we get to number of that size, our brains need to pass it on to computers because we do not possess the capacity or memory to calculate such vast amounts - again it comes back to scale. in the same way we cannot comprehend the planck length or the enormity of the universe. We are of a certain size and anything whether it be a number or our surroundings is only relative in our minds to the size we are0 -
https://en.wikipedia.org/?title=Graham's_number
Just take a look at the Wikipedia page for God's sake. If you have a brain for this then I envy you. I would love to put into context the theory behind this and astro/particle physics0 -
Infinity isn't a number and absolute zero is the lowest possible temperature, nothing to do at maths and it does exist.PL54 said:Obviously infinity is never reached
Absolute zero doesn't exist either, just approximations to it which are called 0
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Absolute zero is more to do with physics/chemistry. If you consider temperature as a measure of thermal motion, then Absolute Zero is the point where no thermal motion takes place.Friend Or Defoe said:
Infinity isn't a number and absolute zero is the lowest possible temperature, nothing to do at maths and it does exist.PL54 said:Obviously infinity is never reached
Absolute zero doesn't exist either, just approximations to it which are called 0
I think people get confused about it not existing as it is pretty much impossible to detect anything at absolute zero, since to measure thermal activity actually requires a tiny degree of thermal activity to take place (the mere introduction of measuring apparatus to an environment that could potentially be absolute zero will cause the thermal activity to rise). Basically it is like being asked to look at something without using light - you know it is there but you are unable to observe it unless some measure of light is hitting your eyes from the object then you cannot perceive it (at least not without equipment).
cabbles - I love Graham's Number. The simple reason for its fame is the fact that it is the largest number ever used in a mathematical proof. It is so large it can never be graphically represented in its entirety in this universe (at least that is what I have read). I mean anyone could come up with a meaningless, really big number but it is actually a number that has a purpose.1 - Sponsored links:
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my anoraks in the dry cleaners at the moment ...............2
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This is the leading candidate for 'Bore of the year thread'.
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If there are some insomniacs a reckon myself and fiiish could cure them! ;-)1
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It is a testament to the human brain. Like I say, I would give anything to be of that intelligence or, rather have a mind that gets maths/science. Imagine working in somewhere like the Perimeter Institute for Theoretical Physics, must be amazingFiiish said:
Absolute zero is more to do with physics/chemistry. If you consider temperature as a measure of thermal motion, then Absolute Zero is the point where no thermal motion takes place.Friend Or Defoe said:
Infinity isn't a number and absolute zero is the lowest possible temperature, nothing to do at maths and it does exist.PL54 said:Obviously infinity is never reached
Absolute zero doesn't exist either, just approximations to it which are called 0
I think people get confused about it not existing as it is pretty much impossible to detect anything at absolute zero, since to measure thermal activity actually requires a tiny degree of thermal activity to take place (the mere introduction of measuring apparatus to an environment that could potentially be absolute zero will cause the thermal activity to rise). Basically it is like being asked to look at something without using light - you know it is there but you are unable to observe it unless some measure of light is hitting your eyes from the object then you cannot perceive it (at least not without equipment).
cabbles - I love Graham's Number. The simple reason for its fame is the fact that it is the largest number ever used in a mathematical proof. It is so large it can never be graphically represented in its entirety in this universe (at least that is what I have read). I mean anyone could come up with a meaningless, really big number but it is actually a number that has a purpose.0 -
Graham's number isn't infinity - it doesn't even approach infinity - because infinity isn't a number, it's an imaginary mathematical construct. Infinity can be represented as one divided by zero (any number divided by zero in fact) - zero isn't a number, again a mathematical construct - so it would follow that infinity cannot be a number.
No different to the square root of -1 also being imaginary (i) but comes in pretty damn useful for example when solving certain quadratic equations!!
Anyway - move on - RD out and all that!
P.S. Negative Kelvin temperatures (below 0 degrees Kelvin) have been detected using ultracold atoms!0 -
Nearly.bobmunro said:Graham's number isn't infinity - it doesn't even approach infinity - because infinity isn't a number, it's an imaginary mathematical construct. Infinity can be represented as one divided by zero (any number divided by zero in fact) - zero isn't a number, again a mathematical construct - so it would follow that infinity cannot be a number.
No different to the square root of -1 also being imaginary (i) but comes in pretty damn useful for example when solving certain quadratic equations!!
Anyway - move on - RD out and all that!
You can't divide anything by zero, but 1/x tends to infinite as x tends to 0. It's represented by a sideways 8 and zero is a number. How many penguins play for Charlton?
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I was watching a programme about infinity that mentioned/referenced Graham's number. It will be on the I-Player, worth a look if you like this sort of thing.bobmunro said:Graham's number isn't infinity - it doesn't even approach infinity - because infinity isn't a number, it's an imaginary mathematical construct. Infinity can be represented as one divided by zero (any number divided by zero in fact) - zero isn't a number, again a mathematical construct - so it would follow that infinity cannot be a number.
No different to the square root of -1 also being imaginary (i) but comes in pretty damn useful for example when solving certain quadratic equations!!
Anyway - move on - RD out and all that!
P.S. Negative Kelvin temperatures (below 0 degrees Kelvin) have been detected using ultracold atoms!
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This only works because 0.999... is treated as an absolute number in that proof. The flaw is that it isn't an absolute number, and whilst you might want to rationalise 10x-x = 9x in that way it isn't actually true because x isn't an absolute. It's fairly obvious that whilst the more 9s you have the closer it is to 1 it will never actually be 1.Callumcafc said:x = 0.99999999...
0.99999999... x 10 = 9.99999999...
therefore 10x = 9.99999999...
10x - x = 9x
9.99999999.... - 0.99999999.... = 9
therefore 9x = 9 and x=1
so 0.99999999... = 1
However, I'm pretty sure that anyone seeing 0.999... will treat it as 1 because it's as near as any number could be. So who cares really.1 -
Not just on this thread either ......Friend Or Defoe said:If there are some insomniacs a reckon myself and fiiish could cure them! ;-)
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I understood zero was invented by the Babylonians as a tipping point from positive to negative. I can accept your point that zero is a number - but it's even!Friend Or Defoe said:
Nearly.bobmunro said:Graham's number isn't infinity - it doesn't even approach infinity - because infinity isn't a number, it's an imaginary mathematical construct. Infinity can be represented as one divided by zero (any number divided by zero in fact) - zero isn't a number, again a mathematical construct - so it would follow that infinity cannot be a number.
No different to the square root of -1 also being imaginary (i) but comes in pretty damn useful for example when solving certain quadratic equations!!
Anyway - move on - RD out and all that!
You can't divide anything by zero, but 1/x tends to infinite as x tends to 0. It's represented by a sideways 8 and zero is a number. How many penguins play for Charlton?
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