Can we get off a frictionless surface by jumping?
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On a friction less surface, you would only be able to jump straight up. Any force applied parallel to the surface would cause you to slip as there is no friction to push against you and keep you from falling over.
You can never make any sideways movement when all you can do is move up and down (and fall over).
What you could do is lie on one's back and take a deep breath, then stand up (a very difficult jump indeed under friction less conditions) and jump into the air. When one is in the air, blow out the air you previously took in...causing you to accelerate in the opposite direction. When you land, since there is no frictional you will keep that motion and continue to slide.
You can never make any sideways movement when all you can do is move up and down (and fall over).
What you could do is lie on one's back and take a deep breath, then stand up (a very difficult jump indeed under friction less conditions) and jump into the air. When one is in the air, blow out the air you previously took in...causing you to accelerate in the opposite direction. When you land, since there is no frictional you will keep that motion and continue to slide.
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