...because it assumes that an infinite sequence of relative frequencies converges to some limit. Unfortunately, the axioms of mathematics do not guarantee that such a limit will exist. It is guaranteed that any bounded infinite sequence must contain a subsequence that converges to a limit; however, there is no guarantee that there is only one limitâ€”the sequence could oscillate forever, and therefore the only way to use this limit as the definition of probability is to first assume that it exists. Therein lies the circularity.
Longrun frequencies cannot be the definition of probability...

Intro metrics books define it exactly like that
Which ones are you reading?
Hill/Griffiths/Lim
Studenmund
Ruud
Davidson
...Mine define it using probability spaces and measure theory.
Those are the technical details, not the meaning.
No, long run frequencies are a consequence of the LLN. The definition is measure theoretic.
Man we should have a basic test for people to post here

Intro metrics books define it exactly like that
Which ones are you reading?
Hill/Griffiths/Lim
Studenmund
Ruud
Davidson
...Mine define it using probability spaces and measure theory.
Those are the technical details, not the meaning.
The formal definition and interpretation of probability are different things. Bayesians and frequentist agree on the formalism. They don't agree on the interpretation.

I know. Too many undergrads. shameful. Used to be an elite place.
Intro metrics books define it exactly like that
Which ones are you reading?
Hill/Griffiths/Lim
Studenmund
Ruud
Davidson
...Mine define it using probability spaces and measure theory.
Those are the technical details, not the meaning.
No, long run frequencies are a consequence of the LLN. The definition is measure theoretic.
Man we should have a basic test for people to post here 
lmao, yeah sure. OP is a clule/ss person.
I love how you can spot the high schooler by some keywords:
"Infinite sequence"
"No guarantee that there is one limit"
"The axioms of mathematics"^note how you can spot the insecure 1styear mathturbator by his uppity attitude

I love how you can spot the high schooler by some keywords:
"Infinite sequence"
"No guarantee that there is one limit"
"The axioms of mathematics"^note how you can spot the insecure 1styear mathturbator by his uppity attitude
Meh, the poster is all right. OP made a doom statement and deserves the booling

OP is not completely wrong.
The heuristic is that empirical frequencies should stabilize and that this should represent the probability. As this can not be formalized in a reasonable way, the important observation was to turn things upside down: Define probability a la Kolmogorov and then PROVE that the empirical frequencies in this model satisfy a LLN. This then "justifies" the axiomatic definition of probability.

OP is not completely wrong.
The heuristic is that empirical frequencies should stabilize and that this should represent the probability. As this can not be formalized in a reasonable way, the important observation was to turn things upside down: Define probability a la Kolmogorov and then PROVE that the empirical frequencies in this model satisfy a LLN. This then "justifies" the axiomatic definition of probability.Ljl

OP is not completely wrong.
The heuristic is that empirical frequencies should stabilize and that this should represent the probability. As this can not be formalized in a reasonable way, the important observation was to turn things upside down: Define probability a la Kolmogorov and then PROVE that the empirical frequencies in this model satisfy a LLN. This then "justifies" the axiomatic definition of probability.Of course he is completely wrong, he is confusing a theorem for a certain class of rvs and a definition.