To approach or exceed the limits of what is possible, acceptable, or safe in order to achieve innovation or progress.
This phrase comes from aviation and aerospace engineering, referring to the 'flight envelope' - the boundary of safe operating conditions for aircraft. Test pilots would literally push against these boundaries to expand what was known to be possible in flight.
The envelope isn't something you mail - it's a mathematical term describing the boundary curve of a family of curves. When Chuck Yeager broke the sound barrier, he was literally pushing the envelope of human flight capability, making this one of the few business clichés with genuine life-or-death origins.
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