i’ve seen a few people leave more algebraic/technical explanations so i thought i would try to give a more handwavy explanation. there are three things we need:
the sum of two numbers doesn’t depend on how those numbers are written. (for example, 1/2 + 1/2 = 0.5 + 0.5.)
1/3 = 0.33…
1/3 + 1/3 + 1/3 = 1.
combining these three things, we get
0.99… = 0.33… + 0.33… + 0.33… = 1/3 + 1/3 + 1/3 = 1.
it’s worth mentioning the above argument could be refined into an actual proof, but it would require messing around with a formal construction of the real numbers. so it does actually explain “why” 0.99… = 1.
i’ve seen a few people leave more algebraic/technical explanations so i thought i would try to give a more handwavy explanation. there are three things we need:
combining these three things, we get 0.99… = 0.33… + 0.33… + 0.33… = 1/3 + 1/3 + 1/3 = 1.
it’s worth mentioning the above argument could be refined into an actual proof, but it would require messing around with a formal construction of the real numbers. so it does actually explain “why” 0.99… = 1.