Your "common sense" version gives the answer of "what man?"
Actually, "what men?", and that is no answer. The group consisting of zero men. Divide the apples between no men? Just scrap the whole idea. (Logically it would also result in infinite apples per man)
Because I can - and to use the basic rule in algebra that dividing and multiplying by the same number results in both operations being simplified out.
Let's look at each side of that equation:
(3/0)x0 = 0
0x0 = 0
Anything multiplied by zero is zero. So both sides are 0. 0=0. Yep. Of course, this doesn't work in your "common sense version"...
Indeed. That's why it results in both 3=0 and 0=0. Or that 19437234589238=0. You can prove everything to be zero if division by zero were a legal operation.
Remember basic algebraic rules:
"multiplying something divided by the same number it is now being multiplied by results in the both operations being simplified out (as in (3/10)x10=3)"
(3/0)x0 = 0x0
Therefore
3=0
Were division by zero a legal operation (that gets an exact, mathematical answer, let's mark it with x), the whole maths would fall apart, see:
3/0=x
Under the algebraic rules (multiplying something divided by the same number it is now being multiplied by results in the both operations being simplified out):
3/0=x
multiply by 0
3/0*0=x*0
simplify
3=0
Divide by zero remains undefined (infinity is not a defined answer either).
No, you've ignored the quite clear explanation.
What explanation?
The probability of rolling a seven in one try is 0/6 (0). The number of tries thus becomes immaterial.
If that wasn't gibberish, which it is. Probability is an expression of two fields. The divisor is the total of all possible outcomes and the numerator is the frequency of the outcomes you're looking at. The two cannot be separated from each other.
The frequency of the outcomes doesn't have to follow the theoretical frequency, though in infinite tries it should - but infinite rolls may always result in getting one, though the probability of that happening is 1-(5/6)^∞=1/∞ (incorrectly marked though, once again, infinity is not an exact term).
"The divisor is the total of all possible outcomes and the numerator is the frequency of the outcomes you're looking at."
Frequency has nothing to do with measuring probability. Theoretical frequency is based on probability (the final probability value tells the theoretical frequency of that exact event whose probability was counted, but the
frequency can't be used in counting probability).
In the case of die rolls there are six possible outcomes of a roll (1, 2, 3, 4, 5, 6). Each individual possible outcome has a frequency of 1 in that field. So the frequency, and numerator, is 1 in the field of six possible outcomes and the divisor is thus 6. 1/6.
If you're looking for a seven, seven has a frequency of 0 in that field. Seven is outside the field of possible outcomes. So the frequency, and the numerator, is 0 and the divisor is... non-existant. Seven doesn't occur in that field so there is no way to express its frequency in the field of outcomes. You won't roll a seven in one try, in six tries or an infinite number of tries - seven is not in that field of outcomes. The probability of rolling a seven is not 0/6. It's 0/? - or 0/every number. Every number, you say? Why, that'd be 0/∞...
Frequency is not the same as probability. Frequency value of an event is (usually) the same as one-roll probability for the wanted event, if there is something to count it from.
If there is only a few rolls, the practical frequency can be and usually is pretty different from the basic probability. Generally it approaches the counted frequency (that is usually the same as the probability of the event happening in one try)
The theoretical frequency of rolling one should be only 1/6, or one in every six rolls, but the probability of always rolling one is g(x)=(1/6)^x, lim(x→∞

g(x)=0, which means it approaches zero never reaching it - it still remains possible though.
Yes, I think that's the problem here. Division by zero is impossible in basic high school math.
And it is impossible, or it still gets no exact answer in very high level maths either. Mathematics is an exact science, not like other science which is fine with dealing with approximations. Infinity is no exact answer, as there is no value that equals infinity - you can always add zero behind it to it to multiply it by ten, for example.
Uh-huh, and how many tries will it take to roll a seven on a standard die?
It can't roll 7.
1-(6/6)^1=0. 0/6=0.
The probability of it rolling seven is 0.
Its theoretical frequency is also 0. So is its practical frequency in this case.
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So, clearly explained:
Rolling one (in one roll) has a probability of 1/6 (1 eligible amongst 6 equally possible possibilities). Therefore that event's theoretical frequency is 1/6, one event in six attempts.
But now, rolling always one has a probability of (1/6)^x = 1/x, x→∞. This event doesn't follow the theoretical frequency, as its practical frequency would be 1. However, we can also count the theoretical frequency for that event (amongst other attempts at rolling infinitely), which is that 1/x, x→∞.
Also, as Exorcet said too, that in infinite rolls rolling will never be finished. That's why rolling a die for infinity and always getting one has a probability infinitely close to zero, however not zero.
Also, this:
No we don't, as there is no proof for anything opposing God either, he doesn't have to have the exact same attributes as in the Bible to exist. As all gods are unfalsifiable (you cannot say there is no god somewhere), all possibilities in the group in which the event of God existing is, are void of any proof, both for and against. Which results in 0/0 (probability for one attempt). For infinite attempts:
d(x)=1-(0/0)^x, x→∞
1 minus infinity? In probability maths that is of no use, as the value has to be between 0 and 1. Therefore no answer.
Also, if you check out things like the Riemann sphere model, it gives infinity to all /0 but 0/0, which remains undefined.
If God is void of any proof, so is every other god and their inexistence too.
Thus why this is a matter of faith, which I've said many times.