setting equal to zero

USAGE SUMMARY

The phrase "setting equal to zero" is correct and usable in written English.
It is typically used in mathematical contexts, particularly when solving equations or functions to find their roots or points of intersection. Example: "To find the x-intercepts of the function, we start by setting equal to zero."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

4 human-written examples

Differentiating with respect to x for and setting equal to zero, we have.

EURASIP Journal on Wireless Communications and Networking

The MSE of (12) can be found by taking its derivative and setting equal to zero.

EURASIP Journal on Advances in Signal Processing

The MSE is minimized by taking its derivative with respect to both G c,b,u (f) and H c,b,v (f) and setting equal to zero in (35) and (36): frac{partial E_{text{MSE}}(f)}{partial G^_{c,p,k}(f)} = 0, (35).

EURASIP Journal on Advances in Signal Processing

(6 Differentiating with respect to s and setting equal to zero gives the MLE s ^ = ∑ t = 0 T − 1 h t (f t + 1 − f t ) 2 ∑ t = 0 T − 1 h t 2 f t (1 − f t ), (7 where h t = f t + h(1 − 2 f t).

Genetics

Human-verified similar examples from authoritative sources

Similar Expressions

56 human-written examples

Often the optical field can be considered to be quasimonochromatic (approximately monochromatic), and then the time delay can be set equal to zero in the above expression, thus defining the mutual intensity function.

Encyclopedia Britannica

In 1932 Einstein and de Sitter proposed that the cosmological constant should be set equal to zero, and they derived a homogeneous and isotropic model that provides the separating case between the closed and open Friedmann models; i.e., Einstein and de Sitter assumed that the spatial curvature of the universe is neither positive nor negative but rather zero.

Encyclopedia Britannica

To find this critical point, the Jacobian matrix should be constructed and set equal to zero.

EURASIP Journal on Advances in Signal Processing

The period before the reform (2001) is set equal to zero.

IZA Journal of Labor Policy

This corresponds to equation (7) with all the θ's and the γ vector set equal to zero.

IZA Journal of Migration

Liquidation causes no uncompensated costs, and thus, (beta _0) can be set equal to zero in the optimal compensation.

Business Research

This is the case for the SW Prony, so for this method, the damping factors are set equal to zero.

EURASIP Journal on Advances in Signal Processing

Expert writing Tips

Best practice

When using "setting equal to zero" in mathematical or scientific writing, ensure that the context clearly indicates why this operation is being performed (e.g., to find critical points, solve an equation).

Common error

Avoid using "setting equal to zero" without explaining the underlying mathematical or logical reason. This phrase is typically used as a step within a larger problem-solving process and requires justification.

Linguistic Context

The phrase "setting equal to zero" functions as a procedural instruction, primarily within mathematical and scientific contexts. It indicates a specific action taken to solve equations or analyze functions, as demonstrated by Ludwig's examples.

Expression frequency: Rare

Frequent in

Science

100%

Less common in

News & Media

0%

Formal & Business

0%

Encyclopedias

0%

Ludwig's WRAP-UP

In summary, the phrase "setting equal to zero" is a grammatically correct and usable phrase, predominantly found in mathematical and scientific domains. As Ludwig AI indicates, it is used as a procedural step in solving equations or optimizing functions. While the frequency of this phrase is rare, its usage is consistent and clear within its specific contexts. Related phrases include "equating to zero" and "making equal to zero", which can be used interchangeably depending on the desired emphasis.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

equating to zero

Emphasizes the action of making something equal to zero, similar in mathematical contexts.

making equal to zero

Highlights the process of forcing a value to be zero.

nullifying the expression

Focuses on making an expression have a zero value.

forcing to be zero

Indicates an active manipulation to set something to zero.

assigning a value of zero

Highlights the action of assigning a zero value.

zeroing out the variable

Specifically targets a variable being set to zero.

driving to zero

Suggests a gradual process towards becoming zero.

setting to nil

Uses "nil" as a synonym for zero, common in programming contexts.

reducing to zero

Emphasizes the reduction of a value until it reaches zero.

making the term vanish

Focuses on causing a term to disappear, effectively becoming zero.

FAQs

How is "setting equal to zero" used in mathematical problem-solving?

In mathematics, "setting equal to zero" is often used to find the roots of an equation or to determine the critical points of a function. By "equating an equation to zero", we can solve for the values of the variable(s) that make the equation true, revealing key properties of the function or system being analyzed.

What does "setting equal to zero" mean in the context of derivatives?

When working with derivatives, "setting equal to zero" helps identify local maxima, minima, or saddle points of a function. These points occur where the slope of the function is zero, and solving the equation formed by setting the derivative to zero reveals their locations.

What are some alternative ways to express "setting equal to zero"?

Alternatives include "equating to zero", "making equal to zero", or "nullifying the expression". The best choice depends on the specific context and the desired emphasis.

Why is "setting equal to zero" important in optimization problems?

"Setting equal to zero" is a crucial step in many optimization problems because it helps find the points where a function reaches its maximum or minimum value. By "finding where the derivative is zero", we can identify potential optimal solutions.