Department of Mathematics
Short proofs in mathematics
Unique factorization
Zorn's Lemma (
dvi file
,
pdf file
, or
postscript file
)
Well ordering of any set (
dvi file
,
pdf file
, or
postscript file
)
Fixed points of increasing functions (
dvi file
,
pdf file
, or
postscript file
)
Hilbert's Nullstellensatz (
dvi file
,
pdf file
, or
postscript file
). See also Bernstein's
summary
, as well as Swan's unpublished
paper
.