¿We said¿ that what we described as “numeral equality”, “being 1-1 correlated”, “having the number n” were widely differing phenomena. That therefore it was an illusion to think that to say “the classes fall in pairs” is, generally speaking an analysis of what we call numeric equality in simpler terms. We can if we like put “being numerically equal” = “falling into pairs” but the use of the one expression just as of the other has got to be explained in the particular case. This we only forget. Thinking about a very special class of examples.
     
The ideas that if they have the right existential structure they do fall into couples & this is demonstrated. The question how we find out in the special case that they do have the right structures is neglected.
     One could also say that a length a was twice another one b if two a superimposed gave b. Application for wavelengths.
     This brings me to the topic of

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demonstration.
     1)
number of outer vertices = 5.

     Compare with “the Hand has 5 Fingers.”
     Timelessness. The same holds of “The number of outer vertices = number of inner vertices”.
     Question which is answered by this proposition timeless. Apparent generality of demonstration.
     The copula has no tenses.
     <…> idea is that the idea of a pentagram is bound up with a cardinal number. Now, we could make all sorts of connections.

“It is the essence of these figures to be capable of being divided|connected in this way”.




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