"not really. you can come up with something in mathematics that has no basis in reality, like an oracle, so that's fine for messing around. but when people use the term "real" to describe numbers they see in the reality, and think of it as some number with infinite number of digits after the decimal, they are maybe missing something. you don't have people going around calling computers oracles. like "oh say you have a computing device in O, the set of oracles", it's retarded. but the real number line is somehow not supposed to be."



This post is pure nonsense.

well what i said was that i think this abstaction of an infinite number of digits after the decimal is kind of nonsense in reality. that is equivalent to saying that the real number line does not exist in reality. if you allow an infinite number of digits after the decimal, with every combination of number, then you have the real line.

you are pure nonsense.

The set of Real Numbers is the set that contains the Rational and Irrational sets. It has nothing to do with "reality" or "oracles" or fairies or unicorns.

We assign definitions to words so that we know what we're talking about. The mathematical definition of "real" is what I posted above. If you don't understand the definition, that's fine; we can explain it. If it's just your opinion that shouldn't be the definition, then I'm sorry you feel that way.

What you are talking about is still an open question that might restructure most of known Math as we know it... IMHO.
http://mathworld.wolfram.com/ContinuumHypothesis.html

actually that's not exactly what we're talking about... that one is if there's something between integers and reals. but we're just talking about reals.

"this abstaction of an infinite number of digits after the decimal is kind of nonsense in reality."

Nobody is disagreeing with that, but that doesn't mean it's nonsense in math. Furthermore, just because something is nonsense in reality doesn't mean it can't be used to describe reality.

Again, I use the notion of the schrodinger equation on an infinite Hilbert space. That doesn't make any sense in reality, and yet we use it every day to describe reality.

well why does the set of reals have to be uncountable? why not just define it as all possible irrational and rational numbers? that's still a countable set.

If you don't like pure mathematics, then I can't do anything about it, but the fact is that all mathematics, including the applied mathematics which you no doubt are more comfortable with, are based on pure mathematics. If you don't like it, suck it up, but if you do maths you will need it. Just like you don't like to do a very boring subject, but you still have to do it to graduate. Sucks to be you.

"I just think it's a bit of a scam to think the set of reals is uncountable, that's all i'm saying. if they are imagining an uncountable set, than they are not imagining reality."

lol omg it IS a semantical argument!

He thinks "real" in mathematics means the same thing as "real" observationally.

ROFL. I think the following sums up bolshoi's argument quite nicely.

http://www.smbc-comics.com/index.php?db=comics&id=2013#comic

irrational numbers are not countable.

the "real" definition in mathematics is NOT IN ANY WAY synonymous with "reality."

You tool.

Real is just a term used so that we have a name for the set of numbers S such that it contains all numbers from the continuous number line, however no. of decimal places it might contain.
You could call it something else, maybe Continuous numbers, maybe Infinitesimal numbers, whatever. So long as it contains those same elements, we can work with that.

and what's wrong with uncountability? what's wrong with having certain sets of numbers have more elements than other sets?

well people will often use the "set of reals" (doesn't actually exist) to do computation. so people are treating numbers from reality as belonging to the set. so there is some connection between the reals and reality in people's minds.

no.
there isn't.
there is only in your mind, and your concepts are wrong.

the set of reals is just to notify that the result can be any number that's from negative infinity to positive infinity. Nothing to do with whether the number exists in some form in real life.

I feel that we are being massively trolled.

I would agree but he's putting way too much effort in. No decent troll would do that. An idiot would, but no real troll.

i'm satisfied with the continuity of rational numbers. i am allowing for certain irrational numbers for the sake that you all seem to like them. but for the real world, you need to express those as a rational in order to perform any computation. so really, for math, all you need are rationals. but even if you had some magical computation device that could have pi to perfect precision and e and all those irrationals, you still wouldn't have the kind of continuity of a real line.

^this is correct. I would just stop responding

oops. That is in response to Gobble's troll comment

Ding! Ding! Ding! Ding! WINNER! You fInally got that nobody will gain anything from this thread and that pretty much only trolls are posting in it.

That was also @gobble.

muted.

*snicker*

so he's gone? ok check out this gem

Gobbledydook (71 )
The irrational set is uncountable. There is a second-order infinity of rational numbers, equal to 2 array of all the integer combinations.
The rational set is uncountable. There is a first-order infinity of rational numbers, equal to the number of integers.

p.s. gobble's gay

@bol

That makes perfect sense to me. Gobble's statement is completely legit.