AWKWARD ZOMBIE

To help with the 0.999... thing:

1/3=0.333...

3(1/3)=0.999...

1=0.999...

Although one argument against this is that 0.999... isn't exactly a number, but a description of the process used to find the number. Obviously, the process of 0.999... goes on forever, and therefore never becomes a number. If you do stop it, you end up with, say, 0.9999, which is definitely one ten-thousandth away from equaling precisely one and therefore not one at all.

Yes, but since you have to apply rounding rules, you have to look at the next number in sequence which is another 9 and have to round up, making it 1 again.

You could also define it with limits:

limn->0(1-n)=1

You could argue that 0.99... isn't a real (or even a complex) number by saying it's just another way to say 1, since R is a unique complete totally ordered field, so two different numbers can never have the same value.

Yep. At a certain number of decimal places, the difference between .999... and 1 becomes so small that it's basically negligible. They're effectively equal.

This is the beginning to a Flash Gordon episode isn't it

Coalmulites from the Ash Planet!

So to carry on from another thread:

Syobon wrote:Uh, explain to me how it could have been made more metric. They made it like that so it's easy to convert, in the vain hope everybody would switch to it. Setting it so that for example 100K=water freezing would have been pointless, as you've pointed out (also, it's dependent on pressure as well, making it even more useless).

The issue with the easily convertible system is that Kelvin probably wouldn't have been adopted ever, since Celsius provides a nice range that anyone can understand and that encompasses the range most people are going to deal with. And we'd be talking about temperatures within a range of 233 and 322 K (-40 to 120 F and -40-49 C) which aren't attractive numbers to laymen (plus they're big enough that differences between the numbers seem negligible). So accessibility shouldn't have been an issue, so the individual degree scale should have followed the same reasoning for what the bottom end of the scale was based on (absolute zero, or lack of heat energy).

Degrees in Celsius were determined by taking the heat energy needed to boil water (in certain conditions, like being at sea level with one atmosphere of pressure) subtracting the heat energy water would need to freeze and dividing the resulting difference by 100 to make a scale. It looks metric because you have a nice even number to deal with, but with Kelvin being based on heat energy, not heat energy relative to an abundant molecule that can have its freezing and boiling point easily determined. The degree scale should have set a scale based on overall heat energy (This substance has one [unit of heat energy], so it is 1 degree Kelvin). You'd still have decimal places (assuming you aren't using the smallest unit of heat energy (which would be stupid, that would be like talking about how tall a building is in nanometers (yes I know there's units smaller than that)).

The degrees wouldn't be based on anything arbitrary (like Fahrenheit) or made from a scale with both extremes based on a specific substance, it has a lower bound and just extends upward indefinitely, with a consistent scale based on the amount of heat energy X contains/produces/etc.

-K-

Mr. Mander wrote:This is the beginning to a Flash Gordon episode isn't it

Coalmulites from the Ash Planet!

It's Mr. Shadow. We have to find the four stones, Leelu, Corben Dallas, and the priest to stop him.

Also Ruby Rhod.

@Kamak,

Sorry bro, but there's a major flaw in your reasoning. Heat energy isn't the same as temperature. They're very related of course. Temperature is a measurement for the movement/vibration of molecules in a substance. Heat energy is basically the sum of all the kinetic energy the molecules posses because of their movement. This means heat energy is dependent on both the temperature and the amount of substance.

E.g., take one liter of boiling water and 10 liter of boiling water. They both have the same temperature, but the later has more heat energy. In your temperature measurement system, this would mean you'd measure the 10 liters of boiling water as being hotter as the 1liter.

Syobon wrote:@Kamak,

Sorry bro, but there's a major flaw in your reasoning. Heat energy isn't the same as temperature. They're very related of course. Temperature is a measurement for the movement/vibration of molecules in a substance. Heat energy is basically the sum of all the kinetic energy the molecules posses because of their movement. This means heat energy is dependent on both the temperature and the amount of substance.

E.g., take one liter of boiling water and 10 liter of boiling water. They both have the same temperature, but the later has more heat energy. In your temperature measurement system, this would mean you'd measure the 10 liters of boiling water as being hotter as the 1liter.

Well yes, the temperature is going to be relative to the heat energy dispersed through the mass of whatever substance you're measuring, that's just require a conversion of total heat energy in the sample divided by total mass of the sample (and probably making some assumptions (like the sample is pure, there's no air in the flask (or the air that is in the flask doesn't matter because it's the same temperature as the sample, so it's not stealing heat), and standard pressure and whatnot). It's basically a simple density triangle, which doesn't negate the usability or reliability of such a measure (assuming the substance is evenly heated, a temperature reading should tell you how much heat energy is in the sample as long as you know the mass, or if you know the mass and know how much heat you're pouring into a substance (and how much is leaking out) you can find the temperature. Don't think you'd use this method though to determine the mass of a substance).

In other words, 1 L of water that is subsequently frozen may have more total heat energy than 5 mL of boiling hot water (contained in a flask), but relative to their masses, the boiling water has more energy per molecule than the frozen water, which means it has a higher temperature.

It's like molarity in acids.

-K-

So, you'd want to set Kelvin so that a rise of one degree in temperature would correspond with one Joule per kilogram energy added? That'd be reasonable I guess.

Syobon wrote:So, you'd want to set Kelvin so that a rise of one degree in temperature would correspond with one Joule per kilogram energy added? That'd be reasonable I guess.

Exactly. It would probably never be practical enough to use in everyday life (like how no one talks in Kelvin now outside of science labs), but it'd be standardized enough to be able to reasonably compare readings and even determine temperature without specifically needing a thermometer.

-K-

Kamak wrote:determine temperature without specifically needing a thermometer

Uh, how and why? It's much easier to measure temperature than energy. I guess you could calculate an increase in temperature if you can estimate how much heat energy you're adding (by burning something and calculating energy release, but the energy released is almost never equal to the energy absorbed by the substance), but you can do that already, you just need a very slightly more complicated calculation.

The only thing such a change in the Kelvin scale would accomplish is that it would simplifies calculations a bit. Although that's neat, most scientists don't care enough about something as trivial as that.

p. cool.