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Next, we define the so-called ''extended alphabet'' or ''bundled alphabet'' E<font face="lucida calligraphy">A</font> as:
Next we define the ''extended alphabet'' or ''bundled alphabet'' <math>\operatorname{E}\mathcal{A}</math> as follows:
: E<font face="lucida calligraphy">A</font> = <font face="lucida calligraphy">A</font> ∪ d<font face="lucida calligraphy">A</font> = {''a''<sub>1</sub>, …, ''a''<sub>''n''</sub>, d''a''<sub>1</sub>, …, d''a''<sub>''n''</sub>}
: <math>\operatorname{E}\mathcal{A} = \mathcal{A} \cup \operatorname{d}\mathcal{A} = \{a_1, \ldots, a_n, \operatorname{d}a_1, \ldots, \operatorname{d}a_n\}</math>
This supplies enough material to construct the ''differential extension'' E''A'', or the ''tangent bundle'' over the initial space ''A'', in the following fashion:
This supplies enough material to construct the ''differential extension'' <math>\operatorname{E}A,</math> or the ''tangent bundle'' over the initial space <math>A,\!</math> in the following fashion:
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