# Yang–Mills and Mass Gap

Discussion in 'Physics & Math' started by Thales, Nov 29, 2017.

1. ### arfa branecall me arfValued Senior Member

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Suppose you construct a set of parallel lines in $\mathbb {R}^2$. Now you mark regularly spaced points along the lines and map the points in adjacent lines to each other. Does it matter if different lines have different spacing? (yes it does, in $\mathbb {R}^2$ because integer arithmetic is based on the integers being separated by unit lengths).

Ok, so suppose you start with a square lattice of points in $\mathbb {R}^2$; How many ways can you construct sets of parallel lines, so you can map points to points between adjacent parallel lines?

3. ### hansdaValued Senior Member

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Is $60 minutes > 1 hour ?$

5. ### NotEinsteinRegistered Senior Member

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You indeed seem to think so.

7. ### hansdaValued Senior Member

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So, maximum $T$ is $1$ unit of time.

8. ### NotEinsteinRegistered Senior Member

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That is indeed your claim. But your claim is inconsistent: if $T$ can at maximum be $1$ hour, then it's maximum is also $60$ minutes, and thus larger than $1$. In other words, if $T$ has a maximum of $1$, it can have a value of $60$, which is a logical contradiction, and thus your claim is proven false. (Tip: Look up "proof by contradiction".)

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