None of what you just said refutes my statements...

Also you don't need calculus to figure out the odds of him showing up during a set time interval. Now if the chance of him showing up at a certain time changes based on some distinct function (can be set or variable) then calculus would be helpful to figure out the odds over a certain interval but from what I can tell it's completely random so calculus is unnecessary.

It's kind of like using a sledgehammer to put nails in a wall. You can do it but it's overkill and far less efficient than other methods. i.e. A ball peen hammer.

Here is the root of the problem ^^^

1/infinity is not defined and you can not say it = 0
it makes as much sense as saying
1/dog = 0, since 1/dog is not defined

however:
the limit 1/x as x approaches infinity does = 0

there is a difference, and it's a very important one.

That's a syntactical issue and only necessary when speaking about calculus. Statistically speaking 1/ ∞ is a very valid value and is equivalent to 0 in the exact same way that 0.999... is equivalent to 1 and for the same reason to boot.

For a more thorough explanation of Almost surely if anyone would like to read about it. http://en.wikipedia.org/wiki/Almost_surely
Please look over the Toin Coss example on the page as it further demonstrates what I was saying earlier. Take note of the following clause:

"The infinite sequence of all heads (H-H-H-H-H-H-...), ad infinitum, is possible in some sense (it does not violate any physical or mathematical laws to suppose that tails never appears), but it is very, very improbable. In fact, the probability of tails never being flipped in an infinite series is zero. Thus, though we cannot definitely say tails will be flipped at least once, we can say there will almost surely be at least one tails in an infinite sequence of flips."

Of course it does. The statistical probability of choosing any specific number is exactly zero when you have an infinite number of numbers to choose from.


There are an infinite amount of times he could show up between noon and 1pm. You have to integrate over that range to include every possible time the mailman could arrive. Calculus is required to get the exact probability of the mailman arriving between two time periods. You can estimate it without calculus, but we're not talking about approximations to solutions. We're talking about actual solutions.

...Which is exactly what I said...




There are not 2 unique time periods. There is 1 time. 12:30 exactly. If you are taking the 12:30-12:31 example then calculus is still not necessary because there is no function to integrate. It's a random variation so all points in time have equal chance of being correct. Thus all you need is basic algebra to solve the equation.

There are 60 one minute intervals in an hour. The chance that he shows up in any specific 1 minute interval is 1/60. There is no reason to use calculus here. Like I stated before, you're trying to use a sledgehamer to put a nail into drywall.

Douglas Adams pointed out the problem with this fallacy in a rather funny way in his imaginary universe:

That's still an approximation of what an integral is and is not an exact solution to the problem described. Is it "good enough" to have a good idea of when the mail man is going to arrive? Sure, but it's still just an approximation nonetheless. To get the exact solution you have to sum all of the infinitesimal time periods been noon and one, and you do that through calculus.

You still fundamentally misunderstand the scenario. If he is showing up between exactly 12:30 and exactly 12:31 then it is not an approximation. It is an exact calculation that he has a 1/60 chance of showing up in that interval.

There is not even any way to integrate over that interval as there is no function to integrate with.

This.

I laughed pretty damn hard at this.