
Academic Guidance Academic Guidance  Academic guidance for those pursuing a college degree... what college? Grad school? PhD help? 
 LinkBack  Thread Tools  Display Modes 
February 8th, 2019, 11:03 AM  #1 
Newbie Joined: Feb 2019 From: Israel Posts: 20 Thanks: 2 Math Focus: general topology  A lemma which is a special case of a theorem
It is often the case that a theorem is called using a lemma which in turn is an easy consequence of the theorem (in other words, is a special case of the theorem). Which term could you suggest specifically for such a lemma? I think about using my own coined word (like "specialia") to denote such lemmas in my book. Is it worth to coin a new word? 
February 8th, 2019, 11:23 AM  #2  
Senior Member Joined: Aug 2012 Posts: 2,424 Thanks: 759  Quote:
A lemma is a minor theorem that helps you prove a major theorem. In written presentations, corollaries come after their corresponding theorem; and lemmas come before the theorem they're helping to prove  
February 8th, 2019, 11:25 AM  #3  
Newbie Joined: Feb 2019 From: Israel Posts: 20 Thanks: 2 Math Focus: general topology  Quote:
 
February 8th, 2019, 01:39 PM  #4  
Newbie Joined: Feb 2019 From: Israel Posts: 20 Thanks: 2 Math Focus: general topology  Quote:
 
February 8th, 2019, 03:32 PM  #5 
Senior Member Joined: Dec 2015 From: Earth Posts: 819 Thanks: 113 Math Focus: Elementary Math 
Call them “tip” or “hint” .

February 8th, 2019, 03:33 PM  #6  
Senior Member Joined: Aug 2012 Posts: 2,424 Thanks: 759  Quote:
But a theorem is generally not an easy consequence of a lemma. Rather, a lemma is kind of a building block. It's something you need to prove along the way to the main theorem; but it's selfcontained enough that you can pull it out. Sometimes because you want to use it for something else; or because it simplifies the narrative flow of the main theorem. It's sort of like the programming practice of pulling out a chunk of code into its own subroutine. You're right, a lemma need not make the main theorem easy. But really it's just terminology, these aren't meaningful distinctions, as the axiom of choice, Zorn's lemma, and the wellordering theorem show. A lot of the naming is historical accident.  

Tags 
case, lemma, special, theorem, writing advice, writing style 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Any special case satisfying $\arctan{\frac{dy(c+s)} {dx(c+s)}}$  whitegreen  Calculus  2  January 21st, 2015 06:01 PM 
Pappus' Theorem Special Case  talisman  Geometry  1  October 27th, 2014 01:05 PM 
Which case is the ambiguous case? Triangle  maxgeo  Algebra  1  October 31st, 2012 03:57 PM 
On the Tietze extension theorem in the metric case.  dionysos  Real Analysis  0  August 27th, 2009 08:40 AM 