# The Monk-Porridge Theorem

What has the above picture got to do with the following mathematical inequality problem?

This inequality looks ... er ... challenging doesn’t it?

We do not know what *x* is, how can we conclude anything?

Think! Think! Think!

...

There is a Chinese idiom 僧多粥少 “many monks, little porridge” which describes a situation of shortage. In economics terms, the *demand* is more than the *supply*. Obviously, if a temple has some hot *steeming* porridge (or gruel) and there are more and more monks coming around, then there is less food to go around for each person. Some of them may go hungry. Maybe a few yet-unenlightened ones can get *steaming* mad and lose their self-eSTEEM. But if there are fewer monks, then each person can have a bigger share.

I formalise this common-sense observation into a mathematical *theorem*, which I call the Monk-Porridge Theorem.

In case you are wondering: what is a “theorem”? In the study of mathematics, a theorem is like a theory-gem. Something which you know for sure to be guaranteed, always true and reliable, and therefore very precious, like gemstones. Since I know it is always true, I can be confident in using it, and it will lead me to a valid logical deduction. OK, it is intuitively obvious. But, how do I know that it is indeed 100% guaranteed confirmed true? How do you know that it always works? We can have a formal proof as follows:-

Assuming *a* to be greater than *b*, we can multiply on the left and on the right by *c*. Because *c* is a positive number, it does not change the direction of the inequality. Now *ab* (*a* times *b*) is also positive. So we can multiply through by *ab*, and the inequality still remains as ‘>’ and does not change to ‘<’. After cancelling, we get . Then we turn this around and say that . Done!

Let us apply this to solve the inequality problem at the beginning.

After factorising (“factoring” in Americanese) the numerator, we look at the denominator. If we changed the denominator from *x*²+1 to *x*², we are dividing by *less*, so we should get *more*. This is true regardless of the value of *x*, because *x*²+1 is always bigger than *x*². Notice now we can cancel away one pair of *x*’s. But that gives us which is what we want!

So today we learned the power of the Monk-Porridge Theorem and see how it can be applied to prove an algebraic inequality.

By the way, there is nothing special about porridge. I could have used pizza and called it the Hungry Children-Pizza Theorem, or perhaps the Cookie Monsters-Cookies Theorem. But you get the idea, yea?

@tradersharpe

-- promoting sharp minds

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qurator (76)4 years agominnowpond (62)4 years ago@royrodgers has voted on behalf of @minnowpond. If you would like to recieve upvotes from minnowpond on all your posts, simply FOLLOW @minnowpond. To be Resteemed to 4k+ followers and upvoted heavier send 0.25SBD to @minnowpond with your posts url as the memo

abay (46)4 years agoMy friend, a kind reminder here.

#cn tag is stand for Chinese.

However, no Chinese was detected in this article.

Please use wisely for your tag,thank you

tradersharpe (57)4 years ago僧多粥少 ;-)

minnowpond (62)4 years ago@eileenbeach has voted on behalf of @minnowpond. If you would like to recieve upvotes from minnowpond on all your posts, simply FOLLOW @minnowpond. To be Resteemed to 4k+ followers and upvoted heavier send 0.25SBD to @minnowpond with your posts url as the memo