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Say, I have two numbers which are almost equal:

A = 1.000000000000000000000001
and
B = 1.000000000000000000000002

What is the right way to say that they are "almost the same"?

  • A is almost B
  • A is almost the same as B
  • A is similar to B
  • A is like B
  • A is alike B
  • A and B are alike
  • A is close to B
  • ?
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closed as not constructive by tchrist, Mitch, Kristina Lopez, MετάEd, Hellion Jun 10 '13 at 16:51

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1  
"Close" and "similar" are relative terms when you're talking numbers. The context of what the numbers represent is important to know before a relative term can be assigned to the two numbers in your example. –  Kristina Lopez Jun 8 '13 at 12:31
1  
You can say ²²⁄₇ and ᴨ are close, but the two numbers you cited are the same the first 24 decimal points, which is far greater precision than anything we can measure. Furthermore, you’re probably getting into floating-point slop in computer calculations. Your two numbers are surely identical within the limits of measurements; they differ only in theory, not in practice. If you are solving a math proof, fine; otherwise, they are as good as equal for anything else. –  tchrist Jun 8 '13 at 12:46
    
@tchrist you are making an assumption about units when you are talking about measurement, what if i told you that A and B are Yotabytes ; we can measure bytes quite accurately and there is a very easily measurable difference between 1.000000000000000000000002 and 1.000000000000000000000001 Yottabytes; –  Ahmed Masud Jun 9 '13 at 8:32
    
@Ahmed Masud The bytes look virtually identical to me. :) –  Mari-Lou A Jun 9 '13 at 11:09

5 Answers 5

up vote 2 down vote accepted

From your list, A is almost the same as B is the best choice. However, A is almost equal to B would be more 'mathematically' correct.

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A is almost B is more mathematically correct, as in mathematics if two things are equal they are exactly the same thing and there were not two things in the first place. "Equal", and "the same" are redundant. –  Lucas Jun 8 '13 at 14:57
    
Hence almost equal... –  ElendilTheTall Jun 8 '13 at 21:03
    
Yes, "A is almost B" would imply "A is almost equal to B", and it is not usually considered wrong to say either. However, there are some who do think it is actually incorrect, though I'm not one of them. But still, saying "A is (almost) equal to B" is like saying "A is more than at least B". –  Lucas Jun 8 '13 at 22:45
    
I up voted the answer because "is almost equal" is used in comparing floating point numbers. I found an interesting link here which backs ElendilThetall's answer. randomascii.wordpress.com/2012/02/25/… –  Mari-Lou A Jun 9 '13 at 11:31
    
"saying "A is (almost) equal to B" is like saying "A is more than at least B"" I disagree, what if A is less than B? –  ElendilTheTall Jun 9 '13 at 12:36

The “right way” to say that A and B are “almost the same” is context dependent. What works in ordinary conversation might not work in conversation among mathematicians, and almost certainly won't work in a mathematical journal paper.

As noted below, two of your forms are acceptable, but none of them are what I would say, which is: “A is nearly equal to B” or “The difference of A and B is tiny”.

In conversation, the forms “A is almost the same as B” and “A is close to B” are acceptable, but except in special contexts, none of the other forms are. That is, for each phrase, one could construct a special or artificial context where that phrase works; but if we assume more-general contexts, we can rule out several of the phrases, as follows. “A is almost B” suggests that A has been changing in value and now is almost B. “A is similar to B”, “A is like B”, and “A and B are alike” suggest that A and B are being compared by some unstated measure of similarity. (In general, “similar” and “like” do not connote a small arithmetic difference, but instead similar bit or digit patterns or other properties.) “A is alike B” isn't grammatical.

Mathematically, almost, almost all, and almost everywhere have specialized meanings; for example:

In set theory, when dealing with sets of infinite size, the term almost or nearly is used to mean all the elements except for finitely many.

“Almost all” is sometimes used synonymously with “all but [except] finitely many” ... or “all but a countable set” ... When speaking about the reals, sometimes it means “all reals but a set of Lebesgue measure zero” ...

In measure theory (a branch of mathematical analysis), a property holds almost everywhere if the set of elements for which the property does not hold is a set of measure zero

Given those specialized meanings, it's reasonable to avoid using almost for almost all other purposes.

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+1 Thanks for articulating so well what I tried to say in my comment! –  Kristina Lopez Jun 9 '13 at 0:54

The difference between the values of A and B is insignificant.

There is no significant difference between A and B.

A and B are equal to 20 significant figures.

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1  
A and B differ in only the least significant figure. –  Wayfaring Stranger Jun 8 '13 at 13:22
    
@WayfaringStranger That's kind of subjective. It depends on how many figures you consider to be "significant". 1 and 2 differ only in the least significant figure, but they're much more different than the numbers given. –  Darrel Hoffman Jun 8 '13 at 15:45
    
I would add: "They are practically the same". I hear this a lot and it makes sense. The two things are so similar that for any practical use of one, the other is usable as well. –  mowwwalker Jun 8 '13 at 16:40
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@DarrelHoffman If I counted correctly, both numbers have 25 sig figs. That being the case the two numbers are objectively identical to within 24 significant figures. Significant figures: en.wikipedia.org/wiki/Significant_figures Of course, you have to be careful, sometimes writers put in more significant figures than the quality of their numbers can justify. –  Wayfaring Stranger Jun 8 '13 at 19:13
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@WayfaringStranger Yes, in this case it's 25 sig figs., but the statement "A and B differ in only the least significant figure" can have widely varying definitions depending on how many figures you consider to be "significant" in any given case. Technically, 1.0*10^100 and 1.1*10^100 also differ by only their least significant figure, but that's a huge difference compared to the original numbers. –  Darrel Hoffman Jun 8 '13 at 23:41

They approximate (to) (each other).

approximation [TFD]

4 (Mathematics) Maths
b an expression in simpler terms than a given expression which approximates to it

[emphasis mine]

verb

approach, near;
come close or be similar to something in quality, nature, or quantity:
a leasing agreement approximating to ownership
a child tries to approximate his parents' speech
I've finally found a vegetarian burger that approximates the taste of real beef.
The colors in the pictures can only approximate the real thing.
an Australian who can approximate a strong New York City accent

syn
approach, compare (with), measure up (to), stack up (against or with), hold a candle to

[var. sources]

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Value of A is almost same as value of B will be right mathematically.

A is almost the same as B from your option list is a good one.

We can also say "Value of A is somewhat near to Value of B".

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