probability - Proof explanation - weak law of large numbers - Mathematics Stack Exchange

Let $(X_i)$ be i.i.d. random variables with mean $\mu$ and finite variance. Then $$\dfrac{X_1 + \dots + X_n}{n} \to \mu \text{ weakly }$$ I have the proof here: What I don't understand is, why it

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real analysis - Proof of the strong law of large numbers for bernoulli random variables - Mathematics Stack Exchange

Laws of Large Numbers (detailed explanation), by Anirudh G

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MathType on X: According to the Law of large numbers, the average of the results obtained from several trials tends to become closer to the expected value as more trials are performed. #

Why is it that proof by contradiction is considered a weak proof

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Laws of Large Numbers (detailed explanation), by Anirudh G

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Law of Large Numbers Strong and weak, with proofs and exercises

Proof of the Law of Large Numbers Part 1: The Weak Law