query: What ordinal number is "the usual real" $\infty$
positive_passages.docid: 22423
positive_passages.text: Which infinity is meant in limits?
negative_passages.docid: 56827
negative_passages.text: Functions that are their Own nth Derivatives for Real $n$
negative_passages.docid: 47871
negative_passages.text: Why did mathematician construct extended real number systems, $\mathbb R \cup\{+\infty,-\infty\}$?
negative_passages.docid: 70196
negative_passages.text: Is there any well-ordered uncountable set of real numbers under the original ordering?
negative_passages.docid: 13018
negative_passages.text: Why is $1^{\infty}$ considered to be an indeterminate form
negative_passages.docid: 16647
negative_passages.text: Is the world $C^\infty$?
negative_passages.docid: 132223
negative_passages.text: Function whose image of every open interval is $(-\infty,\infty)$
negative_passages.docid: 63618
negative_passages.text: Can all ordinals be obtained by taking successors and countable limits?
negative_passages.docid: 52861
negative_passages.text: Natural Numbers and Well ordering
negative_passages.docid: 132140
negative_passages.text: Convergence of Sequence of Real Numbers
negative_passages.docid: 55619
negative_passages.text: What does $\bigcup_{i=0}^{\infty}[i, i+2]$ mean?
negative_passages.docid: 112910
negative_passages.text: Is the set of real numbers really uncountably infinite?
negative_passages.docid: 11586
negative_passages.text: Sequences of Real Numbers in a closed bounded interval
negative_passages.docid: 156727
negative_passages.text: A step in the proof of Characterization of $W^{1,\infty}$
negative_passages.docid: 156978
negative_passages.text: First uncountable ordinal
negative_passages.docid: 107842
negative_passages.text: Behaviour of ($\overline{a}_n)_{n=1}^{\infty}$ and ($\underline{a}_n)_{n=1}^{\infty}$
negative_passages.docid: 154796
negative_passages.text: Completeness of sequence of reals with finitely many nonzero terms