1=0.999... using Cauchy sequences

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In this video I prove that 1=0.999... using the definition of the real numbers as equivalence classes of Cauchy sequences. #math #stem #cauchysequence #realnumbers #realanalysis
  1. Alvaro Lozano-Robledo
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My final year of university I took a real analysis class and it really solidified my understanding of all math classes I took before and I think it was one of the most enjoyable classes I ever took

Sean.Thomas
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Mr. Lozano, in the last step you've missed multiplying by (-1) the right hand side.

The log of a very small number is negative, so it wouldnt make sense to take N as this value. It should be floor(-log_{10}(epsilon))

josemiguel
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A neat thing you learn from this is that there is not a number smaller than one which is greater than or equal to any real number less than one.

SiiKiiN
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Why can we say that N = floor(log_10(epsilon)) works, instead of N = floor(-log_10(epsilon))?

paoloscarpat