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Intangible Assets and Goodwill - Schedule of Intangible Assets (Detail) - USD ($)
$ in Millions
Mar. 30, 2024
Sep. 30, 2023
Finite-Lived Intangible Assets [Line Items]    
Gross Carrying Value $ 5,319.8 $ 5,342.0
Accumulated Amortization 4,567.9 4,453.4
Developed technology    
Finite-Lived Intangible Assets [Line Items]    
Gross Carrying Value 4,389.4 4,411.0
Accumulated Amortization 3,742.2 3,649.5
In-process research and development    
Finite-Lived Intangible Assets [Line Items]    
Gross Carrying Value 21.9 25.7
Accumulated Amortization 0.0 0.0
Customer relationships    
Finite-Lived Intangible Assets [Line Items]    
Gross Carrying Value 601.0 600.0
Accumulated Amortization 561.7 550.6
Trade names    
Finite-Lived Intangible Assets [Line Items]    
Gross Carrying Value 253.0 253.6
Accumulated Amortization 221.0 212.8
Total acquired intangible assets    
Finite-Lived Intangible Assets [Line Items]    
Gross Carrying Value 5,265.3 5,290.3
Accumulated Amortization 4,524.9 4,412.9
Internal-use software    
Finite-Lived Intangible Assets [Line Items]    
Gross Carrying Value 25.5 24.0
Accumulated Amortization 19.4 17.8
Capitalized software embedded in products    
Finite-Lived Intangible Assets [Line Items]    
Gross Carrying Value 29.0 27.7
Accumulated Amortization $ 23.6 $ 22.7