Hello,(adsbygoogle = window.adsbygoogle || []).push({});

Found a book on proofs and went to the exercise section. The proofs are fairly easy. The problem is the question I tried is listed under "direct proofs". I wasn't able to use direct proofs. Here's the question:

For all x in Z, if 2^(2x) is odd, then 2^(-2x) is odd.

My thoughts:

I thought this was a very easy problem because all I had to do was show that 2^(2x)=4^x which is always even and so the proof follows vacuously.

So I wonder why the author listed this problem under "direct proofs" and not under "vacuous proofs" which also has a section of its own. Is there a direct proof ? Is my proof wrong?

Thanks

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Which proof technique is it ?

Loading...

Similar Threads - proof technique | Date |
---|---|

I An easy proof of Gödel's first incompleteness theorem? | Mar 6, 2018 |

I Cantor's decimal proof that (0,1) is uncountable | Sep 27, 2017 |

A A "Proof Formula" for all maths or formal logic? | Apr 19, 2017 |

I Regarding Cantor's diagonal proof. | Feb 28, 2017 |

Hypothesis testing technique | Sep 10, 2014 |

**Physics Forums - The Fusion of Science and Community**