Are there any formulas for min(a,b,c)? [duplicate]

This question already has an answer here:

I was wondering if there are formulas such as min$(a,b)=\displaystyle\frac{a+b-|a-b|}{2}$, etc. but for three numbers (a,b,c).

marked as duplicate by Eric Towers, fonfonx, Hans Lundmark, Namaste algebra-precalculus StackExchange.ready(function() { if (StackExchange.options.isMobile) return; $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() { var$hover = $(this).addClass('hover-bound'),$msg = $hover.siblings('.dupe-hammer-message');$hover.hover( function() { $hover.showInfoMessage('', { messageElement:$msg.clone().show(), transient: false, position: { my: 'bottom left', at: 'top center', offsetTop: -7 }, dismissable: false, relativeToBody: true }); }, function() { StackExchange.helpers.removeMessages(); } ); }); }); Aug 9 '17 at 17:45

$$\min (a,b,c)=\min (\min (a,b ),c)$$
• Why stop there, Salhamam? $\min(a, b, c) = \min(a,\min(b, c)),$ as well. You never appeal to associativity. $\min(a, b, c) = \min(b, \min(a, c))$, acknowledging the the "minimum operator" is commutative as well as associative. – Namaste Aug 9 '17 at 17:51