YAMATO2201
Senior Member
- Joined
- Dec 29, 2016
- Member Type
- Student or Learner
- Native Language
- Japanese
- Home Country
- Japan
- Current Location
- Japan
Does the following sentence sound perfectly natural to you?
★ 2,573,864 is three orders of magnitude greater than 3,745.
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The question above popped into my mind just after I had read the following definition:
order of magnitude
1 if something is an order of magnitude greater or smaller than something else, it is ten times greater or smaller in size or amount
https://www.ldoceonline.com/dictionary/order-of-magnitude
As this definition indicates, we can say "7,000 is two orders of magnitude greater than 70". But what about sentences like ★? The definition seems to me too narrow in scope.
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By the way, I've tried generalizing Longman's definition so that we can accept ★ as a mathematically correct statement:
Proposition For any real number X > 0, there exist a unique integer N and a unique real number A with 1 ≤ A < 10 such that X = A×(10^N).
Notation For any real number X > 0, we denote by ord(X) the unique integer N as appeared in the previous proposition. (I'm not sure if the use of as is correct or not.)
Definition Let X and Y be positive real numbers and n an integer. By definition, Y is n orders of magnitude greater than X if and only if n = ord(Y)−ord(X).
★ 2,573,864 is three orders of magnitude greater than 3,745.
------------------------------------------------------------------
The question above popped into my mind just after I had read the following definition:
order of magnitude
1 if something is an order of magnitude greater or smaller than something else, it is ten times greater or smaller in size or amount
https://www.ldoceonline.com/dictionary/order-of-magnitude
As this definition indicates, we can say "7,000 is two orders of magnitude greater than 70". But what about sentences like ★? The definition seems to me too narrow in scope.
------------------------------------------------------------------
By the way, I've tried generalizing Longman's definition so that we can accept ★ as a mathematically correct statement:
Proposition For any real number X > 0, there exist a unique integer N and a unique real number A with 1 ≤ A < 10 such that X = A×(10^N).
Notation For any real number X > 0, we denote by ord(X) the unique integer N as appeared in the previous proposition. (I'm not sure if the use of as is correct or not.)
Definition Let X and Y be positive real numbers and n an integer. By definition, Y is n orders of magnitude greater than X if and only if n = ord(Y)−ord(X).
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