证明任何实际数字,a、b、a、b、b、0、b^n为O(a^n)、n >=1。
我已经搜索了我拥有的几本关于离散数学的教科书,并对与这一证据有关的类似或核心实例进行了几次在线搜索。 我并不寻求直接的解决办法,但或许可以证明解决证据的适当方法或范式。
如果是,
Prove that for any real numbers, a, b such that a > b > 0, b^n is O(a^n)
然后考虑<代码>O(a^n)的定义。
http://en.wikipedia.org/wiki/Big_O_notation”rel=“nofollow”
1) For f(x), g(x) defined on a subset of reals
2) if there exists some positive **constant** M and real number x_0, such that
3) if ABS(f(x)) <= M * ABS(g(x)) for all x > x_0
In this case f(x) = b^x and g(x) = a^x. I m going to treat this question as if it s a homework question, even though it isn t tagged as one...please correct me if I m wrong!
考虑将脂肪分解成步骤(特别是第3步骤),看看看你是否能够在 任何 x_0, M pair for which is real. 亲爱!
EDIT
I changed f(x) = b^n and g(x) = a^n to f(x) = b^x and g(x) = a^x
<EDIT - HINT
第3步可解释为:
ABS(f(x)) / ABS(g(x)) <= M for all x > x_0
选择你喜欢的固定<代码>M,然后看看你是否能够找到某些<代码>x_0,其中所有x。
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