Algebraic paradox

[Brian WoodParticipant @brianwood45127]

Amusement for the grey matter

[Brian WoodParticipant @brianwood45127]

I found this in an old book of collected Mathematical puzzles selected from Scientific American magazine. It is the leader in my album pictures, I'm not sure how to include it in the text here

The logic appears to be impeccable and it will work if 'c' is assigned the value of zero, but the general expression is compelling. I can imagine it it will appeal to Michael G especially

Enjoy

Brian

Edited By Brian Wood on 05/01/2019 10:05:41

Edited By Brian Wood on 05/01/2019 10:06:31

[John HinkleyParticipant @johnhinkley26699]

Very puzzling! What exactly is the puzzle? Or is that what we're should be trying to figure out? Should even be a challenge for Michael G.

John

[Michael GilliganParticipant @michaelgilligan61133]

**LINK**

https://www.model-engineer.co.uk/albums/member_photo.asp?a=49837&p=820787

… I must leave it 'til later

MichaelG.

[JasonBModerator @jasonb]

Easy enough to work out what the puzzel is even without Michaels help

Edit, beat me to it.

Edited By JasonB on 05/01/2019 10:11:20

[Anonymous]

If c is zero then a-b is also zero so in the first step you multiply both sides by zero – to get 0=0. Just goes to show Kurt Godel was right.

Andrew

[John HinkleyParticipant @johnhinkley26699]

Didn't think to look there!

John

[Gary WoodingParticipant @garywooding25363]

The real answer is that if A=B+C then A-B-C=0, so,

after factorisation you have Ax0 = Bx0, which is clearly correct for all values of A and B

[John HaineParticipant @johnhaine32865]

And it isn't a paradox.

[Andrew TinsleyParticipant @andrewtinsley63637]

The real snag is that you divide both sides by a-b-c which is equal to zero. Dividing by zero is a no, no as the result can have any value.

Andrew.

[pgk pgkParticipant @pgkpgk17461]

As is pointed out a-b-c=0 so as soon as you move ac to the left side of the equation you have 0=0

[GeorgineerParticipant @georgineer]

In my school days we had a proof that any number was greater than any number greater than itself, also achieved by the same trick of a hidden division by zero. There was also a geometrical proof that all right angles are obtuse. Regrettably, the details have evaporated in the ensuing half-century.

George

[not done it yetParticipant @notdoneityet]

Posted by Andrew Tinsley on 05/01/2019 11:05:41:

The real snag is that you divide both sides by a-b-c which is equal to zero. Dividing by zero is a no, no as the result can have any value.

Andrew.

Only zero divided by zero is indeterminate. Zero divided into anything else is actually infinity. The indeterminacy arises because the answer of any number divided by itself is one.

[Tim StevensParticipant @timstevens64731]

And as every schoolboy knows, (to end with a political message) there is nothing more indeterminate than unity.

Cheers, Tim

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