John Valiant wrote:Suppose A is equal to 10
and B is equal to 5.
Then if B is equal to A,
what is B?

If we are allowed to assume a base, then can we say that A equals 10 in base 5. B is equal to 5 in any base greater than 5. This, of course, means that A is equal to B, as 10 in base 5 is equal to 5 in any base greater than 5.

What mathematical notation and theory is this written in?

Ryan McGuire
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Frank Silbermann wrote:What mathematical notation and theory is this written in?

I bet that there is some system where the notation is such that 5 and 10 map to the same thing. Our objective to know which one the OP is thinking of.

For instance...
If we're talking a major pentatonic scale, such as one with notes CDEGA(C), then the "fifth" is a C one octave above the starting note and a "tenth" is a C two octaves above the starting note.

Maybe it has to do tenths of of something circular with a two-ended pointer. For instance, tenths of a circle around a compass. 5 is South and 10 is North. When the needle is pointing North, the other end is pointing South, so North and South and "equal".

I just hope that there isn't some mathematical "proof" that 5 equals 10 involving a division by zero or some other invalid step. That would be disappointing.

Ryan McGuire
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Wait... I know...

When Mr. Valiant is summoning the dark forces from the underworld using mystical symbols drawn in blood on his living room floor, he has to walk around the pentagram twice starting at the corner pointing south. If A is his position after ten "legs" of his trip and B is his position after five, both A and B would have him back at the southern-most point. So... B is "the southern-most point of a pentagram".

Frank Silbermann
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Or, maybe it's clock arithmetic, with a period of five. That is, you count 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 1, ....