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another way of thinking about it:
imagine you have a bottle that contains exactly 1.0L of water. you pour that bottle EQUALLY into three cups. now each cup has .333... L of water. then, you pour each cup back into the original bottle. the bottle now contains
.333...
+.333...
+.333...
----------
= .999... L of water
but we never lost any water, so therefore:
.999 = 1
