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additively

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The answer ADDITIVELY has 0 possible clue(s) in existing crosswords.

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Definitions of additively in various dictionaries:

ADDITIVELY - In set theory, a branch of mathematics, an additively indecomposable ordinal α is any ordinal number that is not 0 such that for any ...

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Possible Dictionary Clues
In an additive manner.
In an additive manner by addition.

Additively might refer to
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 * * * ⋅ * * * ⋅ * * ⋅ * * * * * ...

Additively might refer to

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
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* γ
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* α
*
*
* {\displaystyle \beta ,\gamma <\alpha }
* , we have
*
*
*
* β
* +
* γ
* <
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* .
*
*
* {\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
*
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* β
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* {\displaystyle \beta }
* .
* From the continuity of addition in its right argument, we get that if
*
*
*
* β
* <
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*
*
* {\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
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*
*
* {\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
*
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* =
*
* ω
*
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* ω
*
*
* ω
*
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* ⋅
*
*
* ⋅
*
* ⋅
*
*
*
*
* ...

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