Pull on these motorized boots, activate them, and four small mechanical legs pop out of each sole. The robot legs are half as long as your legs and end in identical smaller boots. Also from these boots pop out four even smaller legs with boots from which extend four miniscule legs, etc.

This fractal
progression continues towards an infinite number of boot sizes with the wonders of existing near-nano mechanization. When you take a one-yard step with a boot, its four legs simultaneously take an additional half-yard step, their legs take quarter yard step and so forth.

The boots will answer the questions: How long is your total stride? How high are your feet from the ground? How much faster can you walk?

I don't think it works that way [UB]. Your solution assumes each row of legs if facing the opposite direction.

I think the example is computed as:

1/2^0 (normal stride)+

1/2^1 (extension from front row of legs) +

1/2^2 +

1/2^3 +

1/2^4 +

1/2^5 +

etc.

Tends to infinity.

Assuming no limitations, the legs would be infinately long, would step an infinately long distance, expending an infinately large amount of energy and a stride would last for an infinate duration.

I agree with UB's take on this. If each successive set of legs steps half the distance of its parent set, you'd never quite make it to twice the stride.

You step a full stride (1). The first set of sub-legs step half a stride (1.5 strides total) then the next step half of that, a quarter-stride (1.75 strides total), then an eighth of a stride (1.875), etc... You'll get infinitely close to 2 strides but never reach it.

Taking it the other way, have increasingly large sets of legs. You would then have something that didn't prove anybody's paradox, but you'd walk incredibly fast.

<david> Haven't you heard of Seven League boots? They feature in many Celtic tales. God knows how they managed to build those in days of yore, though. Maybe after someone makes these legs, they'll invent a time travel machine. That would explain it.........(I've always wondered)