We define a glass of wine W as containing sips w_{0}, w_{1}, w_{2}, …, w_{n}. For two sips w_{n} and w_{m}, n < m if the drinker consumed w_{n} earlier than w_{m}. Note that is <, strictly less than, because if n = m the same sip is being consumed twice. While not unknown, this phenomenon usually does not appear until after more than one glass, and in any case is irrelevant to this study.

We further define a function f, which denotes the flavour of the wine. The better the wine tastes, the larger the value of f. Negative values are regrettably possible.

## The Wine Theorem

The Wine Theorem is simply: f(w_{n}) > f(w_{0})

The proof is left as an exercise to the reader[1].

## Further Conjecture

Conjecture: as n approaches infinity, f(w_{0}) ÷ f(w_{n}) approaches zero.

Attempts to prove this conjecture are not encouraged.

## Conclusion

The last sip of the glass tastes an awful lot better than the first.

[1] the proof is notably simpler when attempted with a glass of cheap wine in hand.