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dasnulium

Infinitesimals and limits are the same thing

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18 hours ago, dasnulium said:

wtf: I did think carefully about word choice for the thesis, in particular I would never use the term 'infinitely small' to describe an infinitesimal - 'indefinitely small' does not mean smaller than 'every' positive number, it means smaller than any positive number to which you can assign a value (this is similar to Kant's ideas about the infinite as discussed by Bell). I don't use the word 'arbitrary' because in numerical analysis (unlike in regular calculus) it means something different to 'indefinite' - namely that the minimum value of the increment may be arbitrary (alternatively, depending on the functions concerned, it may have to meet certain criteria). Note that the term 'indefinitely small' is meaningless for numerical analysis for obvious reasons.

 

> it means smaller than any positive number to which you can assign a value

Can you give an example or an explanation of a positive number to which you can't assign a value? I can't imagine what that could possibly mean. Like 14. I can assign the value 14 to it. What does it mean to assign a value to a number? Isn't the value of a number the number itself? I cannot understand this remark at all.

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