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

in different next

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

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

without loss of generality, we use

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.

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.

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in different next vs without loss of generality, we use