Are these the same?

The image will be sheared such that the x-axis goes through (1,1).

The image will be sheared so that the x-axis goes through (1,1).

I think I have usually seen the former, I didn't even know that “so that” is allowed in English until I once saw it in a text from a (as I assume) native English speaker.


5 Answers 5


The sentences, while very similar, do have a subtle difference of meaning.

"Such that" is a description of HOW something is to be done:

The image will be sheared such that the x-axis goes through (1,1). -> The image will be sheared in such a way that the x-axis goes through (1,1).

"So that" is a description of WHY something is to be done:

The image will be sheared so that the x-axis goes through (1,1) -> The image will be sheared in order for the x-axis to go through (1,1). (Or, more obviously: Because the x-axis needs to pass through (1,1), the image will be sheared appropriately.)

  • 4
    Right. It seems that with "such that", the outcome could just be a coincidence rather than intentional. The cup was tipped such that liquid might spill. The cup was tipped so that one could drink from it.
    – JCooper
    Mar 18, 2011 at 19:33
  • 2
    I think people in the US are generally happier with the shortening of say 'The image will be sheared in such a way that the [new] x-axis goes through (1,1)' to 'The image will be sheared such that the x-axis goes through (1,1)' than people in the UK. I'd say that the preferred ellipsis here is 'The shear required is such that the new x-axis goes through (1,1)'. An adjectival rather than an adverbial. Have you authoritative examples showing the adverbial usage, please? May 13, 2014 at 10:54
  • I just stumbled over this: Paint it red so (that?) people see it vs. Paint it such that people see it – is this the same situation, and can that be used in the first expression? Nov 22, 2015 at 16:34
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    such is an adjective and so an adverb. The former refers to a noun and the latter to a verb. And whereas the clause the x-axis goes through (1,1) refers without a doubt to the verb shear, so is the only right word here. To make it a clause of purpose, add a modal, e.g.: so that the x axis shall go though (1,1). Mar 30, 2017 at 19:38
  • Such is an adverb when used to mean "in such a way." merriam-webster.com/dictionary/such Apr 4, 2018 at 19:03

This distinction criterion is very simple and always works: 'such that' expresses consequence, 'so that' purpose.


I think that 'such that' should refer to a subject noun or pronoun. It is often stretched these days like in example 1, where it is lost upon the reader that it is the image that is such that... at least a comma after 'sheared' could help.

Still, it would be good style to avoid 'such that' without clear subject, just like 'so that' would not be appropriate without a verb.

  • 1
    I agree; I'd prefer 'such that' to introduce an adjectival (see my comment above). I'm prepared to accept the adverbial usage, though; I feel it's a pity no authority for the adverbial usage has been provided. May 13, 2014 at 10:56
  • 1
    I also agree. "So that" introduces a clause that functions as an adverb; "such that" introduces a clause that functions as an adjective. In particular, for the examples in the question, I'd use "so that". Nov 22, 2015 at 22:10
  • Whereas I can't vote, I will express my sincere concurrency in this comment. Mar 30, 2017 at 19:42

I would say “ The image will be sheared such that the x-axis goes through (1,1)” but, as indicated by Hellion, would keep the other construct to express some higher-level aim: “ The image will be sheared so that it is clearer”.


"Such that" is idiomatic mathematical jargon most often used in the definition of mathematical objects. The usage in your example is a bit atypical. The phrase is difficult to directly gloss, but one possible rendering for the phrase as it is used in definitions is "...for which it is true that..."

For example, if we define a rational number as "any p/q such that p and q are integers and q≠0," we've established that iff there are two integers that can be divided by one another to produce a given number, then that number is rational.

Your example is a bit different, because it isn't directly defining a mathematical object, but rather describing a transformation on a mathematical object. (Some branches of mathematics would allow you to define transformations as objects, but that isn't what's being done here.)

By contrast, the phrase "so that" is not mathematical jargon; it's a common-use phrase that indicates the intent or result of some action or condition. Consider the following examples:

  • "I drank coffee so that I could stay awake."
  • "I drank coffee such that I could stay awake."

These sentences are very different! The former sentence is saying that your reason for drinking coffee was to stay awake -- in order to stay awake, you drank coffee. The latter sentence is describing the coffee, not your action of drinking the coffee, saying that it's coffee that you drank before a period of time when you were able stay awake, and suggesting that the coffee had something in it that kept you awake.

Note also that the meaning of the sentence changes yet again when a comma is added as follows:

  • "I drank coffee, such that I could stay awake."

In this case, the phrase "such that" modifies the entire clause in a similar manner to "so that", except it describes the result of your action of drinking the coffee rather than your reason for drinking the coffee. For one reason or another, you drank coffee, and because you drank that coffee, you were able to stay awake. If you ever see the phrase "such that" used outside of mathematics, it will probably be used like this: following a clause, separated from that clause by a comma, and describing the result of whatever is happening in that clause. Your example seems to be using the phrase in this sense, such that the sentence should probably have a comma between "sheared" and "such that".

In particular, this usage often connotes extent, i.e., that the preceding clause is true to an extent that results in whatever's going on in the following clause -- you drank enough coffee to stay awake. This connotation is especially strong if the preceding clause uses some word or phrase that itself describes extent, as in "I drank lots of coffee, such that I could stay awake."

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