[pzhon]

[ QUOTE ]
The concept of infinity is retarded. It does not produce answers that make any sense, it's just theoretical BS.

[/ QUOTE ]
You'll find that mathematicians are not retarded (in fact, we intimidate rocket engineers), and mathematicians have several distinct, very precise, and useful concepts which can be called infinity (ordinals, cardinals, topological compactifications, algeraic infinities, calculus, etc.). The results of logic are not necessarily intuitive, and it is rare for untrained intuition to be good enough to agree with the consequences of dealing with infinity, but infinity is far from BS. Several of the notions of infinity (such as those in calculus) were introduced in order to get sensible answers to concrete problems, and to determine which manipulations of symbols make sense, and which do not.

[ QUOTE ]

For instance, it's mathematically true that .999999 repeating equals 1 (many long stupid arguments have been made, just trust me, according to the rules it does equal 1). Despite the fact that it "should" be less than 1 since it never actually reaches 1,


[/ QUOTE ]
Real numbers don't move or reach for anything. Numbers are not the same as notation. It happens that some numbers have more convenient representations than others, and there may be multiple ways of representing numbers, like 0 and -0.

You could come up with an alternate system of numbers which are based on notation and which wriggle and reach and try. Good luck creating a system as consistent and meaningful as real numbers.

[ QUOTE ]

So you could probably say that with an infinite number of hands, it's long enough to contain any possibility. It's long enough to contain an infinite streak of pocket 9s, as well as infinite streaks of pocket aces and infinite streaks of everything else.


[/ QUOTE ]
You could say that, but you would be wrong. If there is an infinite streak of 99 hands, then after some point, the rest of the hands are 99, and the same is true for an infinite streak of AA hands. These are mutually exclusive. The correct statement is that every finite sequence will occur with probability one.

[ QUOTE ]

Infinity is just an excuse to make up impossible nonsense, but be able to prove it.

[/ QUOTE ]
Infinity can be counterintuitive, but do not confuse your difficulties with intrinsic confusion within the subject.

Proper uses of infinity and infinitesimals simplify models and answers. What is the risk of ruin if you flip an unfair coin an infinite number of times, winning $1 with probability 2/3, and losing $1 with probability 1/3? 1/2^bankroll, and the proof is easy. What is the probability of busting out if you flip that coin only 1,000,000 times, rather than infinitely often? A mess.