Fashionable site I'm changing within last minute (13)

I believe the answer is:

infinitesimal

I'm a little stuck... Click here to teach me more about this clue!

'fashionable site i'm changing within last minute' is the definition.
I can't tell whether this definition defines the answer.

'fashionable site i'm changing within last minute' is the wordplay.
'fashionable' becomes 'in' ('in' can be similar in meaning to 'fashionable').
'changing' is an anagram indicator.
'within' means one lot of letters goes inside another.
'last minute' becomes 'final' (I can't explain this - if you can you should give a lot more credence to this answer).
'site'+'im'='siteim'
'siteim' with letters rearranged gives 'itesim'.
'itesim' placed into 'final' is 'finitesimal'.
'in'+'finitesimal'='INFINITESIMAL'

Can you help me to learn more?

(Other definitions for infinitesimal that I've seen before include "Immeasurably small" , "very little" , "Microscopic" , "Extremely small" , "Minute" .)

I've seen this clue in The Telegraph.

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