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Intangible Assets and Goodwill - Schedule of Intangible Assets (Detail) - USD ($)
$ in Millions
Dec. 30, 2023
Sep. 30, 2023
Finite-Lived Intangible Assets [Line Items]    
Gross Carrying Value $ 5,352.1 $ 5,342.0
Accumulated Amortization 4,519.4 4,453.4
Developed technology    
Finite-Lived Intangible Assets [Line Items]    
Gross Carrying Value 4,419.7 4,411.0
Accumulated Amortization 3,698.9 3,649.5
In-process research and development    
Finite-Lived Intangible Assets [Line Items]    
Gross Carrying Value 22.4 25.7
Accumulated Amortization 0.0 0.0
Customer relationships    
Finite-Lived Intangible Assets [Line Items]    
Gross Carrying Value 602.6 600.0
Accumulated Amortization 559.6 550.6
Trade names    
Finite-Lived Intangible Assets [Line Items]    
Gross Carrying Value 254.1 253.6
Accumulated Amortization 219.0 212.8
Total acquired intangible assets    
Finite-Lived Intangible Assets [Line Items]    
Gross Carrying Value 5,298.8 5,290.3
Accumulated Amortization 4,477.5 4,412.9
Internal-use software    
Finite-Lived Intangible Assets [Line Items]    
Gross Carrying Value 24.9 24.0
Accumulated Amortization 18.7 17.8
Capitalized software embedded in products    
Finite-Lived Intangible Assets [Line Items]    
Gross Carrying Value 28.4 27.7
Accumulated Amortization $ 23.2 $ 22.7