like the x assumed above vs then the sub intervals

These two phrases are not directly comparable as they serve different purposes. 'Like the x assumed above' is used to refer back to a previous assumption, while 'then the sub intervals' is used to indicate a sequence of events or steps. They are correct in their respective contexts.

Last updated: March 08, 2024 • 845 views

This phrase is correct and commonly used in English to refer back to a previous assumption.

"like the x assumed above"

This phrase is used to point out a similarity or connection between the current situation and a previously mentioned assumption.

This phrase is correct and commonly used in English to indicate a sequence of events or steps.

"then the sub intervals "

This phrase is used to show the next step or stage in a process or sequence of events.

Show examples from the web [+]

(iii) if f is non-increasing [respectively, non-decreasing], then the sub-intervals. J, K on the right side in (i) and (ii) may be assumed to have left end-point a.
Then the sub-intervals Bk = (xk,xk−1], for k ≥ 1, and B0 = (x0, 1] are a partition of I. Define {ǫk}k∈N a sequence of positive real numbers, that is strictly mono-.
Then the sub-intervals where qi > (α − 1)π/2 holds are the stable intervals, and the endpoints of these stable sub- intervals where there is a leap of the integral ...

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like the x assumed above vs then the sub intervals