Why do you usually define m+S(n)=S(m+n) but don't m+S(n)=S(m)+n? queha Level 5 user     Posts: 1,194 Threads: 303 Joined: 2016-02-02 #1 2020-04-30 11:58:41 (This post was last modified: 2020-04-30 11:59:19 by queha.) So far I have ever seen the definition of addition of two natural numbers is like: m+0=m m+S(n)=S(m+n) where m, n are both natural numbers, and S(m) is the successor of m. Today I remembered I have never seen some books or whatever defining m+S(n)=S(m)+n. What makes m+S(n)=S(m+n) better than m+S(n)=S(m)+n? For example, let's take 1+1=2. If m+S(n)=S(m+n), then S(0)+S(0) =S(S(0)+0) =S(S(0)). If m+S(n)=S(m)+n, then S(0)+S(0) =S(S(0))+0 =S(S(0)). Whichever you define what m+S(n) equals, it seems you get same result. aaaaaa123456789 Administrator          Posts: 3,577 Threads: 24 Joined: 2015-08-16 #2 2020-04-30 19:42:49 They are equivalents; choosing one or the other is pretty much tradition. If you need to contact me for any reason, or if you have any questions, concerns, problems or requests, message me here or email me at aaaaaa123456789@acidch.at. This forum has been around for (loading...) « Next Oldest | Next Newest » 