From haplotype sequences within each species, we removed indels and excluded infinite-site violations using Map as implemented in SNAP Workbench 2.0 [ 36, 37].
All sequences within one species were collapsed into haplotypes removing indels and excluding infinite-site violations using Map as implemented in SNAP Workbench [ 48, 49].
The mean cluster size, , is the average cluster size to which an occupied site belongs (excluding the infinite percolating cluster, see later).
The point spectrum of H ij, excluding 0, is infinite.
4) The point spectrum of H ij, excluding 0, is infinite.
We still estimate Claus' net worth as infinite, but we excluded him from this year's rankings after being bombarded by letters from outraged children insisting that Claus is "real".
Identical ITS sequences were collapsed into haplotypes using SNAP Map [ 49] after excluding indels and infinite-site violations.
The possibility that some of the presented catemer motifs could belong to large rings rather than infinite chains was considered and excluded.
The possibility is not excluded that a theory may be categorical in some infinite cardinality.
Three genes that were expressed in only one environment were excluded from this regression analysis, because the log2 fold change is infinite.
In fact, it is precisely in the presence of infinite sets that intuitionists drop the classical principle of the excluded third.
