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I was wondering if there is a synonym for the word group "increase by one". Example:

"If the shoe didn't fit, the shoe size was increased by one size."

I think it sounds weird because of the repetition of "size", however, I think I cannot just delete the second "size". So I thought there might be a synonym to give the sentence more variability.

Or does the sentence below sound natural to native speakers?

"If the shoe didn't fit, the shoe size was increased by one."

P.S.: The intended use is a technical publication, so please no colloquial terms or phrases.

P.P.S.: For the offended footlocker headquarter - imagine a series of tubes in your kitchen that come in sizes one, two, three (I hear already plumbers shouting "no, they don't") and the same situation "If the tube was too small to connect with the sink, the tube size was increased by one."

Yup, I got it now, you could say "the next size was chosen" and I will never ask a question here again because obviously this here is native speaker corner and these kind of synonym questions are trivial. So long, and thanks for all the fish.

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    I think it sounds funny for a different reason. The size of a specific shoe (pair) is fixed and cannot be changed to be bigger or smaller. If one is too small, a different (larger) one (pair) must be tried. – Kevin Fegan Jul 7 '18 at 23:41
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    Is the technical publication about fitting shoes to feet? It's often better to use the actual sentence you want to write as an example rather than try to come up with something analogous. The analogy might not work the way you hope it will. – David K Jul 8 '18 at 16:19
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    Nah, the analogy is not misleading. The objects (difficult to describe and would only cause further confusion in this thread) come in predefined sizes and the best fitting size has to be chosen by educated guesses or trial and error. – Mr. T Jul 8 '18 at 16:43
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    When selling boots, I always advise buyers to "go up a size or a half-size". – Bread Jul 8 '18 at 18:28
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    If you want a "technical" term, your example sentence(s) should reflect that. Please edit to include the actual context of your question. – 1006a Jul 8 '18 at 21:56
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Increment, according to Merriam Webster:

the action or process of increasing especially in quantity or value

In programming this is often used to add one, for example in a loop. In your shoe example you are essentially doing the same, you start with some size and increase by one until it fits.

The opposite, if the shoe is too large, is called decrement. You start with some shoe size and try smaller ones until it fits.

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    Good one. I think "...incremented by one" is a concise description. – Mr. T Jul 7 '18 at 14:22
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    @Mr.T Note that one is generally the default increment and may not need to be specified. – chrylis -cautiouslyoptimistic- Jul 7 '18 at 19:51
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    @chrylis In context of shoe sizes, I don't believe it is obvious that one (1) is the default increment. Generally speaking, "increment" means to raise to the next level, and since US shoe sizes increase in discrete units of 1/2, "increment" could mean to increase by 1/2, to the next available size. But, I agree, it could also mean to increase by 1. Here, I would recommend specifying the increment amount explicitly, since ambiguity is generally unwelcome in technical publications. – Gooseberry Jul 7 '18 at 22:56
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    @Gooseberry in a computer science or programming context 1 is the default value when speaking of increment and decrement operators. In another (technical) context or if the reader is not thought to be familiar with them, I agree it's best to define them. Doing that once when first introducing the term should be sufficient. – JJJ Jul 7 '18 at 23:00
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    It's true that in the weird shoe size context, it is unlikely you would use "increment". – Fattie Jul 8 '18 at 18:15
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"Increase by one" is perfectly fine. No need to depart from normal (and in this case precise) English in technical documents. You don't need a fancy word. If you're indeed talking about something abstract, then yes, "increment" might be better but if you don't know that's the right answer it's probably not the right answer.

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    Also, as a native speaker, that second example, "If the shoe didn't fit, the shoe size was increased by one," sounds perfectly natural to me (per the OP's concluding question). – Gooseberry Jul 7 '18 at 23:07
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    @Fattie "With Euro it's a random sequence of numbers." If you mean the "Paris point" - no it is not random. They come with size steps of halves - the larger the number, the larger the shoe. Increasing resp. decreasing, not random. – rexkogitans Jul 9 '18 at 13:53
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    @stumbled on this site — +1 particularly for this pithy gem: ‘ ... but if you don’t know that’s the right answer it’s probably not the right answer’. – NMI Jul 11 '18 at 11:46
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The sample sentence is an odd usage. A normal reference to an increase in size would be “The shoe did not fit so we tried one size larger.”

If indeed the writer is talking in past tense about the instructions they used to follow, then “If the shoe did not fit then one of the next size up should be tried", or perhaps “If the shoe did not fit then one of the next larger size should be tried.”

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    It is just an example sentence. The intended use is technical, not colloquial. – Mr. T Jul 7 '18 at 14:27
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    Indeed, but i thought it an odd enough usage that i suspected it was taken from a special context, and so tried to answer the general issue by using “one larger” and then also tried for an answer to the presumed specific issue. – vulcan_ Jul 7 '18 at 14:39
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I was wondering if there is a synonym for the word group "increase by one".

Yes. There are several, although most of them like 'progress' (orig. "to go up by steps") have taken on expanded senses that obscure the exactness you're trying for. 'Increment' is the closest in current use, but "increasing by one unit on each iteration" is only going to be understood in programming contexts. Otherwise, people are going to take it as the distance between successive steps.

Example:

"If the shoe didn't fit, the shoe size was increased by one size."

Er, no, there's no single word that works there. Even if you used 'progress' or 'increment' there, it's just like 'increase' that you're going to have to specify the increments you're using.

The idiom for this situation is 'go up' or 'down':

"If the shoe doesn't fit, go (up|down) to the next size."

although, given the tentativeness of the proposed solution, it'd also be common to use some version of 'try':

"If the shoe doesn't fit, try the next size (up|down)."

I think it sounds weird because of the repetition of "size"[;] however, I think I cannot just delete the second "size".

You can't. Rephrase to delete the first one, as above.

Or does the sentence below sound natural to native speakers?

"If the shoe didn't fit, the shoe size was increased by one."

No, it doesn't, but not because the second 'size' disappeared. It's unnatural because you're using the past tense to propose tentative solutions—not to report the final answer—but talking about those tentative solutions as though they were final. A one-size adjustment might've still been too (small|large).

If the shoe didn't fit, we adjusted it up or down one size at a time.

with the implication "...until it fit". It's still odd that you're speaking in the past tense in a technical publication where you're presumably speaking generally or providing advice for future action, rather than reporting on your former forays into the fast-paced world of shoe sizing.

P.S.: The intended use is a technical publication, so please no colloquial terms and phrases.

Well, 'go (up|down)' is somewhat colloquial but it's not so informal as 'upsize', '+1ed', &c. It's basic and perfectly clear Germanic vocab that more of your readers will understand than latinate verbiage like 'increment', 'augment', or—Heaven forfend—'decrement' or 'wax greater employing an incremence of one'. As long as you're not trying to stay latinate just to sound smarter, it should be fine.

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Shoe size may be graded in length- perhaps increased by one cm/m or any unit.

Or depending on the situation; the shoe has increased by one than the original size/ by one more than the original size.

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