query: Ordinals: Is $0^\beta = 0?$
positive_passages.docid: 142045
positive_passages.text: What's the definition of limit of sets(esp. ordinals) in set theory?
negative_passages.docid: 378
negative_passages.text: Does $\hat{\beta}=(X′X)^{−1}X′ \ Y$ simplify further?
negative_passages.docid: 24980
negative_passages.text: What is the order when doing $x^{y^z}$ and why?
negative_passages.docid: 39179
negative_passages.text: Why is $(0, 0)$ not a minimum of $f(x, y) = (y-3x^2)(y-x^2)$?
negative_passages.docid: 70418
negative_passages.text: Theorem 3.2 Rudin -- How is 0 concluded?
negative_passages.docid: 158335
negative_passages.text: Why is this $0 = 1$ proof wrong?
negative_passages.docid: 112179
negative_passages.text: Why don't the results of testing $H_0 : \beta = 0$ and $H_0 : {\rm cor}(X,Y)=0$ agree?
negative_passages.docid: 122737
negative_passages.text: How to understand why $x^0 = 1$, where $x$ is any real number?
negative_passages.docid: 106380
negative_passages.text: What is $n!$ when $n=0$?
negative_passages.docid: 106881
negative_passages.text: Does "finite" include zero?
negative_passages.docid: 140086
negative_passages.text: Does $3-4+1$ equal $0$ or $-2$.. or maybe $2$?
negative_passages.docid: 57969
negative_passages.text: Prove that $0$ is not an essential singularity (UW Madison Qualifying exam)
negative_passages.docid: 154356
negative_passages.text: The "difference" of two ordinals
negative_passages.docid: 118232
negative_passages.text: Is it possible for the Lagrange multiplier to be equal to zero?
negative_passages.docid: 117039
negative_passages.text: How to show $(1/n!)^{1/n}$ goes to $0$ as $n$ goes to infinity?
negative_passages.docid: 148927
negative_passages.text: Why does every countable limit ordinal have cofinality $\omega$?
negative_passages.docid: 86866
negative_passages.text: Is there a number whose absolute value is negative?