in different next vs without loss of generality, we use

These two phrases are not directly comparable as they serve different purposes. "In different next" seems to be a fragment of a sentence that is not grammatically correct. On the other hand, "without loss of generality, we use" is a common phrase used in mathematics and other technical fields to indicate that a specific assumption is made for simplicity without affecting the generality of the argument.

Last updated: March 17, 2024 • 741 views

This phrase is not correct in English. It seems to be a fragment of a sentence that lacks proper structure.

"in different next "

This phrase does not make sense in English. It is likely a typo or a misinterpretation of a different phrase.

Show examples from the web [+]

... that is, that taking the same action in the same state on two different occasions may result in different next states and/or different reinforcement values.
... technologies, instruments and software. You have choice in different Next Generation Sequencing technologies, and access to several array-based platforms.
Baylor College of Medicine. 2010 – July 2013 (3 years)HGSC. Work in different Next Gen-Production platforms including SOLiD, Illumina and PacBio.
Apr 10, 2014 ... The methodological improvement presented could benefit the work in different next generation sequencing technologies, where the use of ...

This phrase is correct and commonly used in mathematics and technical fields to indicate a specific assumption made for simplicity without affecting the generality of the argument.

"without loss of generality, we use "

This phrase is used to introduce a simplifying assumption in mathematical proofs or technical discussions.

Examples:

Without loss of generality, we assume that the function is continuous.
Without loss of generality, we can consider the problem in two dimensions.
Without loss of generality, we use a standard coordinate system.
Without loss of generality, we set the initial condition to zero.
Without loss of generality, we consider the case of a square matrix.

Show examples from the web [+]

... of light in vacuum; and V(→r) is an arbitrary external scalar potential; one could easily take it to be quadratic in x and y, without loss of generality. We use.
Without loss of generality, we use. (x1,s(x1)),…, (xk,s(xk)) as k shadows. We can reveal the secret value M by using Lagrange interpolation. where M=s(0).
Jun 3, 2015 ... We consider a variety of μ vectors: (a) the null scenario where all μi=μ0, and without loss of generality we use μ0=0; (b) a “sparse” scenario in ...
Jun 12, 2015 ... Without loss of generality, we use the time unit (min) as the generalized cost unit so that we can minimize the monitoring cost of all incidents.

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in different next vs without loss of generality, we use