Sentence examples for be the same function from inspiring English sources
I mean, if you have a function of x and y, then it will be the same function.
By (L_{q}^{1}(0,a)), (a>0), we mean the Banach space of all functions defined on ((0,a]) such that Vert fVert := int_{0}^{a}biglvert f(t bigrvert,d_{q}t< infty, (2.2) where two functions in (L_{q}^{1}(0,a)) are considered to be the same function if they have the same values at the sequence ({aq^{n}}_{n=0}^{infty}).
None of the two models is strictly more parsimonious than the other: Goalkeeper is more parsimonious with regard to only assuming two factors and mod and resc to be the same function; lock-key is more parsimonious with regard to being independent of factor quantity and not needing to assume net host contributions.
(3) and (4) were not guaranteed to be the same function.
The least squares to minimize are then, adapting equation (1) for a twinned structure, where the weight is usually where w would be the same function discussed in the context of equation (1).
Most of the time it will be the same function as the collar to turn it on.
Let (M x)) and (Omega y)) be the same functions as in Theorem 3.1.
(This means that the two compositions, α ⋅ f and g⋅Fα, are the same function).
Thus there is an e such that d(φe) and φe are the same function.
This was the same function as the main battery's Mk 8 Rangekeeper above except that some of the targets the Mark 1A had to deal with also moved in elevation — and much faster.
