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In mathematics, the least-upper-bound property (sometimes the completeness or supremum property) is a fundamental property of the real numbers and certain other ordered sets. A set X has the least-upper-bound property if and only if every non-empty subset of X with an upper bound has a least upper bound (supremum) in X.
The least-upper-bound property is one form of the completeness axiom for the real numbers, and is sometimes referred to as Dedekind completeness. It can be used to prove many of the fundamental results of real analysis, such as the intermediate value theorem, the Bolzano–Weierstrass theorem, the extreme value theorem, and the Heine–Borel theorem. It is usually taken as an axiom in synthetic constructions of the real numbers (see least upper bound axiom), and it is also intimately related to the construction of the real numbers using Dedekind cuts.
In order theory, this property can be generalized to a notion of completeness for any partially ordered set. A linearly ordered set that is dense and has the least upper bound property is called a linear continuum.
Selling my Wolf A1 14.5 5.56 complete upper. Based on the T91 Service rifle for the Taiwanese Military. Handguard has been slightly modified to accommodate an Mlok Vertical foregrip, cantilever mount for mounting a weapon light, and a QD sling mount. Includes BCM grip, Cantilever...
I'm switching over completely to side-charging uppers, so all of my standard uppers are up for grabs. All have some wear markings, as they have been used. All have <1k rounds through them (many <500). All are complete w/ BCG & CH unless otherwise specified. Asking $280 each, or best offer. In no...
This is a 8.5in barrel with a 10.5in handguard. Less than 100rds through it. Includes the following:
Bolt carrier group
Vortex Sparc II Red Dot
Magpul sling mount
Magpul angled foregrip
*Does NOT include mounted optic or flashlight.
I have a lightly used 10.5in PSA 5.56 pistol upper with a 8.5 slant M-LOK handguard. In great shape, need money for another project. Asking $250 OBO.
Bolt Carrier Group
Feyachi RDS-22 Red Dot Sight
Feyachi Weapon light and Charger
For sale here is a 20 inch upper from Palmetto state. It includes a nitride bcg and milspec charging handle, rifle length gas system.
It's in great shape and has been barely used, it's from a build that I never really shot, has about 300 rounds or less through it.
Original owner, used once Colt EPR complete upper with 14.5" chrome lined barrel, Centurion Arms CMR handguard, Colt upper receiver and Colt BCG/charging handle. I bought a batch of these a few months ago but want to unload a couple before moving. This one was zeroed and tested once (20-30...
AR15 Complete Pistol Upper 11" 5.56
Ballistic Advantage Complete Upper (By Aero Precision)
Pencil profile barrel, R One MLOK Handguard, Rail Grips, Odin Muzzle Device.
Less than 200 rounds through it. 2 range trips.
Reduced: $350 with no BCG.
$450 w/ New BCG
Pickup in Gresham or...
This is a BRN-180S GEN-2 complete upper receiver it has a 223 Wylde barrel, it also includes:
*SB tactical folding buffer tube adaptor
*buffer tube picatinny adaptor
(lower receiver, buffer tube and brace not included)
I fired two 30 round mags through without issue and then moved on to my next...
New, unfired Colt HBPW upper up for grabs. Has a 14.5” SOCOM profile barrel that is factory pinned/welded for 16” OAL. Comes with Colt double heat shield handguards. No BCG or CH but can include a Colt BCG for the buyer for additional $.
$500 local pick up in Hillsboro/Beaverton/Portland...
Im selling my new unfired BCM upper I got a few months ago and never used I installed a Centurion arms m-lok handguard. It comes with a standard charging handle and a mil spec BCG along with a NOS Matech rear sight. This has the socom heavy barrel profile and with the centurion rail it is free...
Up for sale/trade is this brand new 16” Daniel Defense DDM4v11 complete upper chambered in 5.56. Haven’t even sent one down the pipe and pretty sure I still have the box. Cleaning out the safe and she has sat for too long. I’m open to trades for equal or maybe even lesser value depending on the...
Complete upper build from AR-15discounts. Also selling a Sig MSR Red Dot for $80 but if you want to buy it with this I'll take $20 off the red dot as a package. This has had 1 mag through it and everything functions well. Just going another route and don't need this sitting around.
Aero Precision M4E1 16" 5.56 M4 Complete Upper Receiver w/ ATLAS S-ONE Handguard Black
Less than a thousand rounds down range. Functions flawlessly.
AR15 Gen 2 Assembled Upper Receiver
ATLAS S-ONE 15" Handguard M-lok with front and rear picatinny rail
16" 5.56 CMV Barrel with 1/7 twist and...
Decided to go another route so I’m selling my upper.
Aero Precision M4E1 upper
Geissele MK8 13.5 mlok rail
Radian raptor charging handle
14.5” Rosco barrel
Dead air flash hider/ suppressor mount
The upper was put together buy Curts custom shooters in Milwaukie.
10.5 inch Barrel with VG6 Epsilon 9mm Muzzle Device (total length 12.25 inches)
7.25 inch Yankee Hill Machine KeyMod Handguard with Ergo Wedgelok Rail Covers
Fail Zero Bolt Carrier Group
Mil-spec Charging Handle
Selling a complete PSA nitride uppper with a Aero Precision BCG and MI quad rail in tan/FDE with magpul accessories willing to trade also for a 9mm pistol depending on the quality and brand of the pistol plus cash on my end also good red dots or LPVO thank you.