3 ms·
Depending on the nature of the problem and the proof technique, sometimes it can be (from a little to much) easier to prove something is no greater than or no l
by seanhunter 3y ago
Depending on the nature of the problem and the proof technique, sometimes it can be (from a little to much) easier to prove something is no greater than or no less than a certain bound than proving what exactly it is. For example it's trivial to prove using triangles that the square root of two is somewhere between 7/5 and 3/2 but proving exactly the value of root two is quite a lot harder.
- pletnes 3y agoIndeed - a classic «upping the game» is to prove two bounds, then determine an exact value because you somehow get the bounds to intersect. https://en.wikipedia.org/wiki/Squeeze_theorem?wprov=sfti1 https://en.wikipedia.org/wiki/Squeeze_theorem?wprov=sfti1
- burnished 3y agoHell yeah, squeeze theorem! I was so enchanted when I first learned this one that everyone I knew also learned about the squeeze theorem. Sorry, nothing substantial to add, I just got excited about it again