arbitrary sum

USAGE SUMMARY

The phrase "arbitrary sum" is correct and usable in written English.
It can be used in mathematical or statistical contexts to refer to a sum that is determined by random choice or is not fixed. Example: "In our calculations, we will use an arbitrary sum to demonstrate the variability of the results."

✓ Grammatically correct

Science

News & Media

Encyclopedias

Human-verified examples from authoritative sources

Exact Expressions

1 human-written examples

At your fair price, you should be indifferent between taking either side.[6] de Finetti speaks of "an arbitrary sum" as the prize of the bet on E. The sum had better be potentially infinitely divisible, or else probability measurements will be precise only up to the level of 'grain' of the potential prizes.

SEP

Human-verified similar examples from authoritative sources

Similar Expressions

59 human-written examples

Since (mathsf{Ind},mathcal {C}_0 rightarrow mathsf{Ind},mathcal {C}) commutes with arbitrary colimits, e commutes with arbitrary sums.

Bulletin of Mathematical Sciences

This argument can be quite powerful if one is independently motivated to deny arbitrary sums, and goes along with denying Unrestricted Mereology.

SEP

The functor e has a right-adjoint functor (e^dagger ), thus commutes with arbitrary sums, and then since e is conservative, this implies that h also commutes with arbitrary sums.

Bulletin of Mathematical Sciences

Since (C_cdot ({text {Ab}})) has arbitrary sums, so does the category ({text {DCoalg}}(C_cdot ({text {Ab}}),Q)).

Bulletin of Mathematical Sciences

The category (mathsf{StHom}) has arbitrary sums, and it has the following remarkable property: for any triangulated category ({mathcal {D}}) with arbitrary sums, a triangulated functor (nu :mathsf{StHom}rightarrow {mathcal {D}}) that commutes with arbitrary sums admits a right-adjoint (nu ^dagger ) (this is a part of Brown Representability Theorem).

Bulletin of Mathematical Sciences

Since (mathcal {C}) has finite coproducts, (mathsf{Ind},mathcal {C}) has arbitrary coproducts, so that ({text {Ho}}(mathsf{Ind},mathcal {C})) has arbitrary sums.

Bulletin of Mathematical Sciences

See section 3.2 of the main entry for more discussion on the denial of arbitrary sums (see van Inwagen 1981 as well for a rejection of the "Doctrine of Arbitrary Undetached Parts").

SEP

end{aligned} (10.9)In general, the functor (10.8) is triangulated, and it commutes with arbitrary sums, so it admits a right-adjoint functor (H^dagger ) by Brown representability.

Bulletin of Mathematical Sciences

Moreover, since e commutes with arbitrary sums, the full subcategory in ({text {Ho}}(mathsf{Ind},mathcal {C}_0)) spanned by objects (E') with ({text {Hom}}(E',widetilde{E})) is closed under sums, and then by Lemma 12.7, it coincides with the whole ({text {Ho}}(mathsf{Ind},mathcal {C}_0)).

Bulletin of Mathematical Sciences

Officials "threatened, pressured and forced the Africville residents to agree to the compensation being offered by the City of Halifax" and paid them arbitrary sums for their land, court documents state.

Vice

Expert writing Tips

Best practice

When using "arbitrary sum" in technical writing, define the context in which the sum is considered arbitrary. For instance, clarify whether it refers to a sum chosen without a specific rule, or one that can take any value within a defined range.

Common error

Avoid assuming that an "arbitrary sum" is unimportant. In many mathematical and statistical contexts, an arbitrary value is used to demonstrate generality or to establish a baseline for comparison. Its arbitrariness doesn't diminish its analytical value.

Linguistic Context

The phrase "arbitrary sum" functions as a noun phrase, where "arbitrary" modifies the noun "sum". It typically denotes a sum that is chosen without any fixed rule or specific reason. Ludwig's examples show this usage in diverse fields like mathematics and philosophy.

Expression frequency: Uncommon

Frequent in

Science

60%

Encyclopedias

20%

News & Media

20%

Less common in

Formal & Business

0%

Wiki

0%

Reference

0%

Ludwig's WRAP-UP

The phrase "arbitrary sum" is a grammatically sound and usable English expression. It refers to a sum that's not predetermined or fixed, often chosen freely for the sake of generality. As confirmed by Ludwig, this phrase is correct. It finds its primary usage in technical fields such as mathematics and science, though it occasionally appears in news and philosophical contexts. While some might confuse "arbitrary" with "unimportant", it's essential to recognize its significance in demonstrating general properties or establishing comparisons. Alternatives like "random total" or "unspecified total" may suit different contexts.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

random total

Emphasizes the unpredictable nature of the total, suggesting it's derived from a random process.

unrestricted summation

Emphasizes the absence of limitations on the summing process.

unspecified total

Highlights the lack of a defined or known total value.

chance accumulation

Focuses on the sum arising from random or unplanned events.

variable aggregation

Focuses on the process of summing, where the components can change.

flexible compilation

Highlights adaptability in the process of accumulating values.

determined quantity

Focuses on the quantity that is found with no rules applied.

indefinite amount

Shifts the focus from summing to a general, non-specific quantity.

non-specific quantity

Similar to "indefinite amount", but more general, applicable outside of summing.

discretionary allocation

Highlights the freedom to assign sums based on individual choices.

FAQs

How can I use "arbitrary sum" in a sentence?

In mathematical proofs, you might say, "Let's consider an arbitrary sum of series to demonstrate convergence properties." In finance, one could state, "The model allows for the allocation of an arbitrary sum to various investment portfolios."

What are some alternatives to "arbitrary sum"?

You can use alternatives like "random total", "unspecified total", or "variable aggregation" depending on the context.

Is it more appropriate to say "arbitrary amount" or "arbitrary sum"?

While both are grammatically correct, "arbitrary sum" is typically used when referring to the result of addition or accumulation. "Arbitrary amount" is more general and applies to any unspecified quantity. See also "indefinite amount".

What does it mean for a mathematical constant to be defined through an "arbitrary sum"?

Defining a mathematical constant through an "arbitrary sum" suggests that its value can be represented as a sum of terms, where the choice of terms might not follow a strict, predetermined rule, allowing for generality or exploration of possible values. This could also allow for "discretionary allocation" during the calculation.