Can a number ever be small enough to be considered zero?

Suppose you went to the worlds worst casino, "Infinite Odds". To win you had to pick an exact number, from 1 to a quadrillion (or any number). Not only that, but you had to do it a quadrillion times in a row. I know that I can multiply this out to get a '1 in X' times this will happen, X being pretty large.

Here is my question, given infinite trials, you can make the trial sample large enough to make whatever outlandish odds actually become a favorite to happen.

Given enough trials, '1 in X', no matter how large, becomes a favorite to happen.

In mathmatics, is there an accepted number that effectively becomes zero, even though given enough time you could express it?

Secondly, does anyone know of any medication for weird drifting thought patterns?

[Siegmund]

That depends on who makes the first move. If the casino announces fixed odds, you can choose a number of trials great enough that you are likely to win. If, on the other hand, you announce how many times you are willing to play, they can create a game with bad enough odds you are unlikely to win.

But there is no "one size fits all" number which can be names as "close enough to be considered zero." It's a case by case analysis to determine how small of a number, if any at all, is negligible for a particular type of mathematical question.

In mathematical proofs you will often see phrases like "for sufficiently large N," which is a shorthand for a particular condition -- usually something like "if you first specify the maximum size of error you will tolerate and call it delta, I can name an N beyond which you're guaranteed to always come closer than delta to the answer."

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Here is my question, given infinite trials, you can make the trial sample large enough to make whatever outlandish odds actually become a favorite to happen.

Given enough trials, '1 in X', no matter how large, becomes a favorite to happen.



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This is a mathematics beyond me (it doesn't take much anyway). Would you be kind enough to explain what you mean by a longshot becoming a favorite (if I understood it correctly)? Thanks.

[MCS]

If you play the lottery, you probably won't win. If you play the lottery every day for a trillion years, you almost certainly WILL win.

That being said, I'm not really sure what relevance this idea has to the OP's question.

In answer to the OP: I am not 100% sure what you are asking, but the product of a finite number of positive numbers is positive (and thus not zero). Weird things happen if you start thinking about trying to multiply an "infinite" amount of numbers.