assertion does not hold

USAGE SUMMARY

The phrase "assertion does not hold" is correct and usable in written English.
It can be used in contexts where you are discussing the validity or truth of a statement or claim, indicating that it is not supported by evidence or reasoning. Example: "After reviewing the data, we found that the assertion does not hold true in this case."

✓ Grammatically correct

Science

News & Media

Human-verified examples from authoritative sources

Exact Expressions

3 human-written examples

Suppose that this assertion does not hold.

Fixed Point Theory and Applications

If the assertion does not hold, then we can assume that there exists a constant C satisfying (Vert f_{n} Vert _{L^{p}(dmu }leq C).

Journal of Inequalities and Applications

Despite some support in humans, this assertion does not hold over the range of different natural animal species where cancer incidence is known.

Evolutionary Applications

Human-verified similar examples from authoritative sources

Similar Expressions

56 human-written examples

The following example shows that the converse assertions do not hold.

Fixed Point Theory and Applications

Hence, it is obvious that every -function is a -function and every -function is a -function, but the converse assertions do not hold.

Fixed Point Theory and Applications

We will first show that there exists a positive number t 0 such that the equation H 1 ( t, s, x ) = 0 (2.2). has no solution x in D ( C ) ∩ ∂ Ω for all t ∈ ( 0, t 0 ] and all s ∈ [ 0, 1 ]. For s = 0, assertion (2.2) is obvious because ( T t + ε J ) x = 0 implies x = 0. Assume that assertion (2.2) does not hold for any s ∈ ( 0, 1 ].

Journal of Inequalities and Applications

If w0 ∈ X and the assertion (A1) does not hold, then (A2) holds.

Fixed Point Theory and Applications

Let w0 ∈ X be arbitrary and fixed and suppose that the assertion (F1) does not hold.

Fixed Point Theory and Applications

The chief constable repeated his assertion that policing "does not hold the solutions alone" to the union flag dispute and he called for renewed political talks on the issue.

BBC

For example, as illustrated in Fig. 4, when CW = 20, the simulated maximum stable throughput of 2.12 Mbps is far larger than the saturation throughput of 0.65 Mbps, while the mean total packet delay is only around 2 ms. Note that the assertion (a) in [21] generally does not hold true because this assertion is drawn from simulations based on constant-bit-rate (CBR) traffic.

EURASIP Journal on Wireless Communications and Networking

Fixing w 0 ∈ ( 3, 5 ), by (4.7), we get that the sequence ( w m = T [ m ] ( w 0 ) : m ∈ N ) is not left convergent to 3 and 3 ∉ M ( w 0 ) = ( 3, 6 ] and thus, for J = p, the assertion (B2) of Theorem 2.1 does not hold.

Fixed Point Theory and Applications

Expert writing Tips

Best practice

When using the phrase "assertion does not hold", ensure you provide clear reasoning or evidence to support why the assertion is invalid. This strengthens your argument and enhances credibility.

Common error

Avoid stating that "assertion does not hold" without providing specific reasons or evidence. Simply making the statement without justification weakens your argument and may lead to misinterpretations.

Linguistic Context

The phrase "assertion does not hold" functions as a negation of a proposition. It's used to refute a claim or statement, indicating that it is not valid or true. Ludwig AI confirms its acceptability in written English.

Expression frequency: Common

Frequent in

Science

60%

News & Media

20%

Formal & Business

10%

Less common in

Encyclopedias

3%

Wiki

3%

Reference

2%

Ludwig's WRAP-UP

The phrase "assertion does not hold" is a common and grammatically sound way to express that a statement or claim is invalid or untrue. Ludwig AI confirms this. Primarily found in scientific and news contexts, its function is to negate a proposition and challenge its validity. To use it effectively, provide clear reasoning or evidence. While alternatives like "the claim is invalid" or "the statement is false" exist, "assertion does not hold" carries a tone of thorough examination. Remember to avoid overgeneralization without providing supportive evidence when using this phrase.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

the claim is invalid

Uses "claim" instead of "assertion" and replaces "does not hold" with "is invalid".

the statement is false

Replaces "assertion" with "statement" and "does not hold" with "is false".

the premise is incorrect

Substitutes "assertion" with "premise" and "does not hold" with "is incorrect".

the argument is flawed

Replaces "assertion" with "argument" and "does not hold" with "is flawed".

the hypothesis is disproven

Uses "hypothesis" instead of "assertion" and "is disproven" instead of "does not hold", implying a more formal rejection.

the proposition is untenable

Replaces "assertion" with "proposition" and "does not hold" with "is untenable", suggesting the statement cannot be defended.

the belief is unfounded

Substitutes "assertion" with "belief" and "does not hold" with "is unfounded", indicating a lack of supporting evidence.

the conclusion is unsupported

Replaces "assertion" with "conclusion" and "does not hold" with "is unsupported", suggesting a lack of evidence for the derived result.

that's not the case

A more general way of saying something is not true or valid.

this is simply untrue

A straightforward way of saying that something is not correct.

FAQs

How can I use "assertion does not hold" in a sentence?

You can use "assertion does not hold" to express that a statement or claim is not valid or supported by evidence. For example, "After analyzing the data, it became clear that the assertion does not hold."

What are some alternatives to "assertion does not hold"?

Alternatives include phrases like "the claim is invalid", "the statement is false", or "the premise is incorrect", depending on the specific context.

Is it better to say "assertion does not hold" or "assertion is incorrect"?

Both phrases are acceptable, but "assertion does not hold" often implies a more detailed examination or analysis has led to the conclusion, while "assertion is incorrect" is a more direct statement. The best choice depends on the context and the level of detail you want to convey.

What does it mean when someone says an "assertion does not hold"?

It means that the assertion or claim being made is not true, valid, or supported by the available evidence or reasoning. It suggests there's a flaw or weakness in the original statement.