query: Could there be a -1 dimension?
positive_passages.docid: 52827
positive_passages.text: Could negative dimension ever make sense?
negative_passages.docid: 41651
negative_passages.text: Volume bounded by a sphere of radius $1$ in 4 dimensions
negative_passages.docid: 65230
negative_passages.text: Expressing points in fractional dimensions?
negative_passages.docid: 131128
negative_passages.text: Why time is considered a dimension?
negative_passages.docid: 15971
negative_passages.text: Are units of angle really dimensionless?
negative_passages.docid: 27198
negative_passages.text: Not an essential singularity
negative_passages.docid: 156636
negative_passages.text: The Existence of the $^1D$ term and the non-existence of the $^3D$ term?
negative_passages.docid: 144771
negative_passages.text: Is there any thing composed of elementary particles in this world that is not 3 dimensional?
negative_passages.docid: 63516
negative_passages.text: $C^1[0,1]$ is not complete with respect to sup norm
negative_passages.docid: 45485
negative_passages.text: Dimension of a subset
negative_passages.docid: 86667
negative_passages.text: Is the 1-Dimensional Lie algebra Simple?
negative_passages.docid: 124631
negative_passages.text: Why are we not able to visualize Dimensions beyond 3 (or maximum 4 including time)?
negative_passages.docid: 57070
negative_passages.text: Dimensionality of null space when Trace is Zero
negative_passages.docid: 82097
negative_passages.text: If $A \succeq B$, is it true that $B^{-1} \succeq A^{-1}$?
negative_passages.docid: 140576
negative_passages.text: Time reversal symmetry and T^2 = -1
negative_passages.docid: 72416
negative_passages.text: The universe appears to have a lower bound in the time dimension, why not an upper bound?
negative_passages.docid: 26769
negative_passages.text: Why does string theory require 9 dimensions of space and one dimension of time?