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No, "0.333..." is an exact representation. The "..." is part ... three recurring", which is even more transparently an infinite series.)

The sequence 0.3, 0.33, ..., 0.333... has a limit of 1/3 as the number of digits grows without bound. That's not the same as saying it *is* 1/3.

No, the sequence 0.3, 0.33, 0.333, 0.33, ... has limit 0.33.., which is (notation for) the decimal expansion of 1/3.

J.

You and me both, man. However, in the archives are ... to the group not to go down that path again.

I don't remember everything I learned in my probability and statistics classes forty years ago, but I do seem to ... But if N is, say, ***, then the probability is 10**-100, which is close enough to zero for government work.

Odd that you should mention (Emil) Borel, who argued that events with such small probabilities are effectively impossible. The time you'll have to wait until such an event happens is larger by far than the age of the universe.

J.

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Odd that you should mention (Emil) Borel, who argued that events with such small probabilities are effectively impossible. The time you'll have to wait until such an event happens is larger by far than the age of the universe.

George Gamow in his wonderful book "One Two Three...Infinity", worked out the probability of all the air in a room suddenly rushing to one corner, leaving the reader to suffocate in his chair. Another not impossible event you'd have to wait a long time to see happen.

dg (domain=ccwebster)

Sure you can. Throw it ten times in the first minute, then 10 times in the next thirty seconds, and so on. You'll be done in two minutes.

Nope. As my die throwing rate approached the speed of light, time would have to slow down to accomodate me. Two minutes would never arrive so how could be done then?

Okay,I* can't do it, and *youcan't do it, but that says more about us than about the mathematics of the situation.

dg (domain=ccwebster)

It's actually identical. In the die case, the sequence (S) is simply "6". The point is that in an infinite ... will be zero. In any finite number of trials, there will be a non-zero probability of the sequence not occurring.

So you are saying that at some point in a sequence of trials, the non-zero result of raising a number from the set (0..1) to a power equal to the number of trials, becomes zero?

dg (domain=ccwebster)

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BTW, is the notation with dots over the repeating decimals still used? As in . 0.3 = 0.333... . . 0.12345 = 0.123452345...

I've never seen dots used. I learned it (30 years ago) with a line over the repeating digits: 0.3 = 0.333... 0.12345 = 0.123452345... but I don't know if that's still taught.

I was taught to put the repeating digits in parentheses.

0.1(2345)

I don't know where that was (Latvia? Germany? Back in the "old days" at SJSC?), but I just found a document stating that it is done in Portugal, not that I ever was there.

Skitt (in Hayward, California)

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Odd that you should mention (Emil) Borel, who argued that events with such small probabilities are effectively impossible. The time you'll have to wait until such an event happens is larger by far than the age of the universe.

In my humble opinion, I think you've made a misstatement.

You can't say that you "have to wait" a long time for an event with probability zero to happen. It could happen in the next instant.

If we ask someone to pick any integer, the probability they will pick 2,117,489,316,237 is "zero", but it's not impossible that they would pick exactly that number immediately.

Consider the example I gave in another reply:

throwing a die infinitely many times without a six coming up is possible (all throws being independent)

but it has probability zero.

Sorry to disagree but you can't throw a die "infinitely many" times, no matter how long you try. At every point in your sequence of throws, there is a 5/6 probability of not throwing a six. For any number of throws, n, (5/6)^n is a positive, non- zero, number.

You also can't throw a die a google times, no matter how hard you try. Bet you can't even personally do a billion.

Richard Maurer To reply, remove half

Sunnyvale, California of a homonym of a synonym for also.

throwing a die infinitely many times without a six coming up is possible (all throws being independent)

but it has probability zero.

Sorry to disagree but you can't throw a die "infinitely many" times, no matter how long you try. At every point in your sequence of throws, there is a 5/6 probability of not throwing a six. For any number of throws, n, (5/6)^n is a positive, non- zero, number.

You also can't throw a die a google times, no matter how hard you try. Bet you can't even personally do a billion.

Richard Maurer To reply, remove half

Sunnyvale, California of a homonym of a synonym for also.

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I was just thinking about this the other day, and since a good example drifted by on another ng, I thought I'd bring it up.

I sometimes see "finite" used where a meaning of "greater than zero" seems intended, rather than one of "not infinite". An example came up in a discussion of life near the Arctic Circle: "since the sun has a finite angular diameter, the night and day durations are asymmetric". I think I've also heard similar usages from mathematicians. Comments?

Turns out that it is not that new. My AmHer(1969) has this listed separately from the mathematical senses:

finite: 2. Being neither infinite nor infinitesimal.

My question is what did people use before 'finite' to mean the same thing. Did "a definite amount" or "a certain amount" do the job?

Richard Maurer To reply, remove half

Sunnyvale, California of a homonym of a synonym for also.

I sometimes see "finite" used where a meaning of "greater than zero" seems intended, rather than one of "not infinite". An example came up in a discussion of life near the Arctic Circle: "since the sun has a finite angular diameter, the night and day durations are asymmetric". I think I've also heard similar usages from mathematicians. Comments?

Turns out that it is not that new. My AmHer(1969) has this listed separately from the mathematical senses:

finite: 2. Being neither infinite nor infinitesimal.

My question is what did people use before 'finite' to mean the same thing. Did "a definite amount" or "a certain amount" do the job?

Richard Maurer To reply, remove half

Sunnyvale, California of a homonym of a synonym for also.

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