Let's have an argument - Argh it keeps recurring!
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acemuzzy wrote:2.9 is less than 3 (by 0.1), yes. 2.99 is also less than 3 (by 0.01). 2.999... is less than 3 by 0.000...
Exactly, so it's less! So 2, 2.999..., 3.
This one was easy to figure out, ngl
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mistercrayon wrote:Diluted Dante wrote:Basically, it's a made up number.
The thing is all of the numbers are. The ancient romans managed fine without a 2.
I heard that 12 is a common number for totalling stuff (or something) due to counting on a hand in the good old days, 3 parts to a finger etc. Dunno if it's true but it made sense to me when I heard it.
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LivDiv wrote:The maths theory allows for infinitely accurate division that must be mirrored with infinite recurring numbers.
The real world (,like putting stuff on scales) isnt like that.
If you divided something by 3 in reality you will end up with one piece eventully being bigger/heavy/longer whatever.
Your three pieces would be...
0.33...3
0.33...3
0.33...4
No, if you divide something exactly by 3 in the real world you would have 3 3rds. Which would equate to 3 x 0.333..., which would =1 -
nick_md wrote:mistercrayon wrote:Diluted Dante wrote:Basically, it's a made up number.
The thing is all of the numbers are. The ancient romans managed fine without a 2.
I heard that 12 is a common number for totally stuff (or something) due to counting on a hand in the good old days, 3 parts to a finger etc. Dunno if it's true but it made sense to me when I heard it.
The babylonians (and possibly the sumarians) had a counting system based around 60. That's why there are 60 seconds in a minute and 60 minutes in an hour. -
GooberTheHat wrote:LivDiv wrote:The maths theory allows for infinitely accurate division that must be mirrored with infinite recurring numbers.
The real world (,like putting stuff on scales) isnt like that.
If you divided something by 3 in reality you will end up with one piece eventully being bigger/heavy/longer whatever.
Your three pieces would be...
0.33...3
0.33...3
0.33...4
No, if you divide something exactly by 3 in the real world you would have 3 3rds. Which would equate to 3 x 0.333..., which would =1
You have missed the point.
Its impossible to divide something infinitely accurately in real life. -
LivDiv wrote:GooberTheHat wrote:LivDiv wrote:The maths theory allows for infinitely accurate division that must be mirrored with infinite recurring numbers.
The real world (,like putting stuff on scales) isnt like that.
If you divided something by 3 in reality you will end up with one piece eventully being bigger/heavy/longer whatever.
Your three pieces would be...
0.33...3
0.33...3
0.33...4
No, if you divide something exactly by 3 in the real world you would have 3 3rds. Which would equate to 3 x 0.333..., which would =1
You have missed the point.
Its impossible to divide something infinitely accurately in real life.
No its not, its just impossible to accurately represent it as a decimal. -
Actually, it is possible, but just not intuitively so.
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GooberTheHat wrote:Actually, it is possible, but just not intuitively so.
Eventually you will get down to a level of accuracy that involves splitting atoms and then you've got much bigger problems. -
Sure, but then we're just getting silly. Or we get mummy monkey in to make sure it's equal and end up with nothing.
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For sure but its useful to explain the difference between real world and math theory which is where I think people are getting stuck i.e Nick's scales.
Maths allows for infinity, the real world doesnt. Most people approach things in real world terms because they aren't Maths undergrads. -
nick_md wrote:
Exactly, so it's less! So 2, 2.999..., 3. This one was easy to figure out, nglacemuzzy wrote:2.9 is less than 3 (by 0.1), yes. 2.99 is also less than 3 (by 0.01). 2.999... is less than 3 by 0.000...
Lol. But it's less "by zero", so not actually "less". I mean 4 is -1 less than 3 so uh woo. -
acemuzzy wrote:nick_md wrote:
Exactly, so it's less! So 2, 2.999..., 3. This one was easy to figure out, nglacemuzzy wrote:2.9 is less than 3 (by 0.1), yes. 2.99 is also less than 3 (by 0.01). 2.999... is less than 3 by 0.000...
Lol. But it's less "by zero", so not actually "less". I mean 4 is -1 less than 3 so uh woo.
Tell it to the scales, my man.
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DrewMerson wrote:How does asserting that 0.999r = 1 sit with the old problems of swimming pools / running tracks, where with each burst you cover 99% of the remaining distance? That also describes 0.999r, but it is generally accepted that infinite bursts will never reach the end. Can’t have it both ways, surely.
https://en.wikipedia.org/wiki/Zeno's_paradoxes is the usual framing of this. But uh clearly you do reach the end (or have you never swum a length?) so I don't get your point. If you're saying you wait 30s between each burst, then sure that way you'd never get to the end, but that's a different problem, rather than a contradiction. -
Much of maths, particularly anything to do with inifinity, cannot necessarily be applied to the real world.
https://backreaction.blogspot.com/2020/12/is-infinity-real_5.htmlBut is infinity real? Does it exist? Well, it arguably exists in the mathematical sense, in the sense that you can analyze its properties and talk about it as we just did. But in the scientific sense, infinity does not exist. -
DrewMerson wrote:Edit: Am I wrong to say that always covering 99% of the remaining distance means that my distance covered is 0.999r?
No I think that's correct. Until you hit the wall. -
If this was a real thing then the finiteness of atoms will come into play I think. If it’s a pure maths thing then sure it won’t ever hit the imaginary edge.
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DrewMerson wrote:But you can’t ever hit the wall if you only ever cover .99 of the remaining distance. Do it an infinite number of times, and you cannot hit the wall, because there’s always, always 1% of the distance not covered.
In theory yes that would go on for an infinite amount of time/iterations.
In reality obviously you wouldn't be able to accurately travel 0.99 times the distance you did the last time because of all the variables and their tolerances like muscle, shoes, the surface etc. At some point you will accidently cross the line. -
I think that 99% thing is not the same as 0.9r. 0.9r is one, it’s just a bad way of writing it. The paradox is good at emphasising the confusing nature of irrational numbers like pi. 0.9r is not irrational.iosGameCentre:T3hDaddy;
XBL: MistaTeaTime -
What?iosGameCentre:T3hDaddy;
XBL: MistaTeaTime -
tigersgogrrr wrote:Does that mean 0.3r is actually 0.4 then...
No. -
Yeah ok. I suppose the next discussion needs to be on the definition of infinity. You can still prove it converges on 1 as a sum to infinity so I suppose it works, I just don’t think it’s a helpful way of thinking about it.iosGameCentre:T3hDaddy;
XBL: MistaTeaTime -
Nah you're still not viewing this right. It's got nothing to do with the realism of doing it or thickness of atoms etc.
Say (for the sake of easy maths) the pool is 100m long and you swim 1m/s.
Clearly it takes 100s to swim it.
Or equally, diving it your way, it takes:
- 99s for the first 99m
- 0.99s for the next 99% of what's left
- 0.0099s for the next 99%
- etc etc
So it *doesn't* take infinite runner, so the time for each next but is getting smaller and smaller.
And the answers have to be the same, cos we just expressing the same thing in two different ways.
ie 100s = 99 + 0.99 + 0.0099 + ... = 99.999r and we're back at what I said before THEY ARE THE SAME THING
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