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When is distance reduced to 0?

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When two objects gets closer to each other, you can measure the distance between the two of them, and see how that value gets smaller and smaller and smaller. Soon you'd be working in decimals such as 0.8mm, 0.1mm, 0.000000001mm etc, but obviously using smaller measurement terms. Now my question is, how much can we reduce that distance by, before we can say they are now touching, and the distance between the two objects is 0? What's the value that comes just before it reaches 0?