Additive number theory | Wikipedia audio article
Channel: wikipedia tts
Date: 29/12/2018

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Additive_number_theory


00:01:26 1 Additive number theory
00:04:02 2 Additive combinatorics
00:05:43 3 See also



Listening is a more natural way of learning, when compared to reading. Written language only began at around 3200 BC, but spoken language has existed long ago.

Learning by listening is a great way to:
- increases imagination and understanding
- improves your listening skills
- improves your own spoken accent
- learn while on the move
- reduce eye strain

Now learn the vast amount of general knowledge available on Wikipedia through audio (audio article). You could even learn subconsciously by playing the audio while you are sleeping! If you are planning to listen a lot, you could try using a bone conduction headphone, or a standard speaker instead of an earphone.

Listen on Google Assistant through Extra Audio:
https://assistant.google.com/services/invoke/uid/0000001a130b3f91
Other Wikipedia audio articles at:
https://www.youtube.com/results?search_query=wikipedia+tts
Upload your own Wikipedia articles through:
https://github.com/nodef/wikipedia-tts
Speaking Rate: 0.787341480998457
Voice name: en-AU-Wavenet-D


"I cannot teach anybody anything, I can only make them think."
- Socrates


SUMMARY
=======
In number theory, the specialty additive number theory studies subsets of integers and their behavior under addition. More abstractly, the field of "additive number theory" includes the study of abelian groups and commutative semigroups with an operation of addition. Additive number theory has close ties to combinatorial number theory and the geometry of numbers. Two principal objects of study are the sumset of two subsets A and B of elements from an abelian group G,

  
    
      
        A
        +
        B
        =
        {
        a
        +
        b
        :
        a
        ∈
        A
        ,
        b
        ∈
        B
        }
      
    
    {\displaystyle A+B=\{a+b:a\in A,b\in B\}}
  ,and the h-fold sumset of A, 

  
    
      
        h
        A
        =
        
          
            
              
                
                  A
                  +
                  ⋯
                  +
                  A
                
                ⏟
              
            
            h
          
        
        .
      
    
    {\displaystyle hA={\underset {h}{\underbrace {A+\cdots +A} }}.}
  There are two main subdivisions listed below.