Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
General question on function growth
#1
I've been reading this explanation.

Now take functions
f(x) = x^x
g(x) = (x + 1)^(x + 1)

According to the definition of "little-oh", I'd conclude that f(x) = o(g(x)).

Am I right?
Reply
#2
(03/08/2011, 07:37 AM)dyitto Wrote: I've been reading this explanation.

Now take functions
f(x) = x^x
g(x) = (x + 1)^(x + 1)

According to the definition of "little-oh", I'd conclude that f(x) = o(g(x)).

Am I right?

Yes, because f is not : if you would chose any constant C>0 (> 0 is essential though omitted in that text, better look at wikipedia), then you always find
x^x < C (x+1)^(x+1) for large enough x
because
x^x / (x+1)^(x+1) < (x+1)^x / (x+1)^(x+1) = 1/(x+1) < C
Reply
#3
Intuitively I would say that the above functions f and g have about the same growth rate, since f simply stays one step behind g.
A function with a REAL different growth rate would be:

h(x) = x^(x^x)

So if I wanted to look into the relative growth of hyperoperational functions, then these Bachmann–Landau notation apparently wouldn't be of much use in this context.
Reply


Possibly Related Threads...
Thread Author Replies Views Last Post
  Composition, bullet notation and the general role of categories MphLee 7 384 02/06/2021, 12:01 AM
Last Post: JmsNxn
  Kneser method question tommy1729 9 6,432 02/11/2020, 01:26 AM
Last Post: sheldonison
  New mathematical object - hyperanalytic function arybnikov 4 4,066 01/02/2020, 01:38 AM
Last Post: arybnikov
  Is there a function space for tetration? Chenjesu 0 1,478 06/23/2019, 08:24 PM
Last Post: Chenjesu
  A Notation Question (raising the highest value in pow-tower to a different power) Micah 8 7,833 02/18/2019, 10:34 PM
Last Post: Micah
  Degamma function Xorter 0 1,889 10/22/2018, 11:29 AM
Last Post: Xorter
  Math overflow question on fractional exponential iterations sheldonison 4 6,999 04/01/2018, 03:09 AM
Last Post: JmsNxn
  Between exp^[h] and elementary growth tommy1729 0 2,038 09/04/2017, 11:12 PM
Last Post: tommy1729
  Sexp redefined ? Exp^[a]( - 00 ). + question ( TPID 19 ??) tommy1729 0 2,560 09/06/2016, 04:23 PM
Last Post: tommy1729
  Should tetration be a multivalued function? marraco 17 26,061 01/14/2016, 04:24 AM
Last Post: marraco



Users browsing this thread: 1 Guest(s)