Scrabble?! ADDITIVELY

Is additively valid for Scrabble? Words With Friends? Lexulous? WordFeud? Other games?
Scrabble (US/Canada)
Yes! (68 pts)
Yes! (54 pts)
Yes! (68 pts)
Yes! (68 pts)
Yes! (68 pts)
Yes! (10 pts)
Yes! (68 pts)
Yes! (71 pts)

Definitions of ADDITIVELY in various dictionaries:

In set theory, a branch of mathematics, an additively indecomposable ordinal α is any ordinal number that is not 0 such that for any β , γ < α {\displaystyle \beta ,\gamma <\alpha } , we have β + γ < α . {\displaystyle \beta +\gamma <\alpha .} Additively indecomposable ordinals are also called gamma numbers. The additively indecomposable ordinals are precisely those ordinals of the form ω β {\displaystyle \omega ^{\beta }} for some ordinal β {\displaystyle \beta } . From the continuity of addition in its right argument, we get that if β < α {\displaystyle \beta <\alpha } and α is additively indecomposable, then β + α = α . {\displaystyle \beta +\alpha =\alpha .} Obviously 1 is additively indecomposable, since 0 + 0 < 1. {\displaystyle 0+0<1.} No finite ordinal other than 1 {\displaystyle 1} is additively indecomposable. Also, ω {\displaystyle \omega } is additively indecomposable, since the sum of two finite ordinals is still finite. More generally, every infinite cardinal is additively indecomposable. The class of additively indecomposable numbers is closed and unbounded. Its enumerating function is normal, given by ω α {\displaystyle \omega ^{\alpha }} . The derivative of ω α {\displaystyle \omega ^{\alpha }} (which enumerates its fixed points) is written ϵ α . {\displaystyle \epsilon _{\alpha }.} Ordinals of this form (that is, fixed points of ω α {\displaystyle \omega ^{\alpha }} ) are called epsilon numbers. The number ϵ 0 = ω ω ω ⋅ ⋅ ⋅ ...

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There are 10 letters in ADDITIVELY ( A1D2E1I1L1T1V4Y4 )

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