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[MonkeyHead]

There's zero chance of your chosen integer being infinity because it's not an integer

Indeed. It's a fruit, even though people usually tend to treat it as a vegetable.

That's why it goes in salads.

[Frumple]

Infinity salad sounds like something out of a horror story, ngl. Shit's probably half cut with soylent green and claiming to be vegetarian despite being 50% long pork by weight.

[hector13]

Infinity salad sounds like something out of a horror story, ngl. Shit's probably half cut with soylent green and claiming to be vegetarian despite being 50% long pork by weight.

If the human was vegetarian, they’re not technically lying.

[Putnam]

Actually, in statistics there is the concept of "almost all" or "almost none".

Say you have an infinite set A where there are an infinite amount of 1s but, say one or two or a thousand 2s. Intuition says that you have zero probability of picking a 2 if you randomly picked an element. But actually you have an almost zero probability of picking a 2. So, 0 for practical purposes but for some mathematical functions the distinction matters.

Mathematicians are a pedantic bunch.

The probability there is actually, literally 0, not "almost 0". Actually, perhaps more interestingly, it's worse than that: the integers are a countable set. If we ask the question "what's the chance of picking a prime number from a uniform distribution over the integers?", the answer is "undefined, because there is no uniform distribution over the integers". For any arbitrary integer X, the following applies: "almost all integers are not X, so there's 0 chance of picking X". Since the integers are countable, you just sum up the probabilities, so 0+0+0+0... ends up with 0. Turns out, probabilities are actually way easier to work with in uncountable sets, it's wild.

[MaxTheFox]

My head hurts

[voliol]

Wait, would not "any even number"  have the same probability to be picked then? Equals zero. That does not seem right. Is there something "wrong" with the question, that makes it different from "what proportion of all integers have the property X"?

[Magmacube_tr]

maiy pipi hört

[martinuzz]

You might need to see a ürölögîst then

[Mathel]

Wait, would not "any even number"  have the same probability to be picked then? Equals zero. That does not seem right. Is there something "wrong" with the question, that makes it different from "what proportion of all integers have the property X"?

If you were to pick a random integer between 0 and infinity (which is indeed not an integer, it's not even a number), the chance of it being even is 0.5⁺. 0 is an even number so in any set of consecutive integers starting with 0, there is either equal number of even and odd numbers, or one more even than odd.

With primes, it gets more interesting. We could try it the brute-force way. We know that in an infinite number of positive integers, there is an infinite number of numbers. Also, an infinite number of those are primes.
This results in the chance of getting a prime being infinity/infinity, which is undefined.
So let's try a different way.
The Prime Number Theorem says that the number of primes equal to lower than R (and we can easily substitute N for R) is roughly R/(ln (R)).
Since we are operating in natural numbers, that becomes N/(ln(N)). The number of natural numbers equal to or lower than N is N.
So the chance of a random number between 1 and N being a prime is (N/(ln(N))/N), which can be simplified to 1/(ln N).
Since ln (N) limits to infinity at infinity, 1/ln(N) limits to 0 at infinity.

As such, the chance of a random integer between 1 and infinity is indeed 0⁺, a chance so low, that it might as well be 0, but not actually 0.

[Akura]

Went to the doctor for my (hopefully the last) colitis treatment, where they took some blood for testing as usual. As I was leaving, they had to do a quick finger stick because my blood sugar read unusually low. Not sure why my blood sugar dropped that low, I would have expected the opposite. The second test came back normal.

[Eric Blank]

You know what makes me feel like a caveman? Having to find some makeshift tool with which to accomplish a task because it's impossible to do by hand and I'm not provided the necessary tools and training.

Today, for work, it was scraping sticky gunk off of the freezer shelves. And the implement I settled upon was one of the aluminum tag plates from a hanging product peg. Because the rough frozen surfaces just would not abide a paper towel with vinegar water on it. Nor the skin of my knuckles as it turns out.

Stuffs still stuck on there good. What we should really do it pull them out and defrost them and scrub them with dish soap, but that would take hours longer than I have on my schedule.

[heydude6]

The tool you want for that is a paint scraper or putty knife. I used one all the time to clean off gunk when I volunteered at a thrift store. We had a very robust set of janitorial equipment, and I ended up adding a bunch of new nouns to my vocabulary as a result.

[King Zultan]

I've had to improvise tools quite a few times.

[Flying Teasets]

500 error

[Putnam]

As such, the chance of a random integer between 1 and infinity is indeed 0⁺, a chance so low, that it might as well be 0, but not actually 0.

No, no, it's actually 0. From 0 to X it's proportional to 1/log(X), but "at infinity" it's 0, actually, factually 0. The density of the primes in the integers is 0, in other words. Not 0 with caveats.

Wait, would not "any even number"  have the same probability to be picked then? Equals zero. That does not seem right. Is there something "wrong" with the question, that makes it different from "what proportion of all integers have the property X"?

There is no uniform distribution over the even integers, yes. But in any range from 0 to N, the proportion's going to be about 0.5; it never really leaves the vicinity of 0.5, and in fact stays closer and closer as N increases, so it approaches 0.5 as it approaches infinity, so (as it goes) it's 0.5.