Proving that 1/8 Is Larger Than 1/4

Yep, you’ve read that right.

Here we go (log below means log10, so log with base 10):

3 > 2
3 log(1/2) > 2 log(1/2)
log[(1/2)³] > log[(1/2)²]
(1/2)³ > (1/2)²
1/8 > 1/4

Convinced? If not, what’s wrong with the proof above?

Click to see solution

Credit: I saw the above trick on a lesson by prof. Arnaldo Viera Moura at Unicamp.

One thought on “Proving that 1/8 Is Larger Than 1/4

  1. Ali Asghar

    The proof is wrong because multiplying both sides by log(1/2) is exactly like multiplying by a negative number so it reverses the relation sign……..


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