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2

Despite having been down-voted this is a perfectly valid question. Divergent (or better: asymptotic) series are a very common phenomenon in physics. People like Michael Berry have spent large parts of their research career on this topic (see e.g. Item 6 on asymptotics, plus links therein, on his homepage). Useful review articles are for instance the ones by ...

2

"The answer is that since we are proud physicists and not nitpicking mathematicians we will just wing it when the need arises" This quote is taken from A. Zee's Quantum Field Theory in a Nutshell, and it summarizes the attitude of physicists to mathematics. (At least in an undergraduate level) Since we are physicists, most of our mathematics isn't rigorous. ...

-2

first of all your question seems to me very ambigous in technical context of physics and mathematics after all what type of combinations you are talking about regarding to yogurt?if we want to try combinations of yogurt with many things like : yogurt with salad,frozen yogurt ice cream,yogurt beverages like ayran ,greek yogurt based dish tzatziki( i think ...

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Whether you have a finite number of pieces is not the important part, it is the relationships they may have to one another. Consider a point proton and an electron with a perfect $1/r$ potential without second quantization and at zero Kelvin (no temperature). There are an infinite number of energy eigenstates, so there are an infinite number of different ...

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After adding a large but finite number of atoms, the yoghurt will collapse into a black hole. After that point, the flavour will not change, no matter what new atoms you add, because Black Holes Have No Hair. So, no, the number of combinations is finite. On the other hand, it is large enough that there isn't enough space in the visible universe to write ...

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All possible combinations or permutations of a finite amount of "stuff", will always be finite. This is a basic fact from combinatorics. Details Number of ways to select $k$ things from a set of $n$ things: $\mathcal{C}(n,k)=\frac{n!}{k!(n-k)!}$, where $m!$ means $1\times2\times3\dots m$. Reference. Here order does not matter Number of ways to permute ...

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I accept Mustapha's point for discrete systems, the problem is that we don't know if the amount of matter the universe is discrete (i.e. finite combinations) or continuous (i.e. infinite combinations). Say you added differing ranging amounts of food items. For example, apple, strawberry, and kiwifruit. Then, to me at least, there is no limit to the ...

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I'd like to point out that Springer has published a book on this subject. It really seems an interesting read: Leo Corry: David Hilbert and the Axiomatization of Physics (1898–1918), From Grundlagen der Geometrie to Grundlagen der Physik. $\quad \quad \quad \quad \quad \quad \quad \quad\quad$

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