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Summary of Significant Accounting Policies - Schedule of Intangible Assets (Details) - USD ($)
$ in Millions
Sep. 28, 2024
Sep. 30, 2023
Finite-Lived Intangible Assets [Line Items]    
Gross Carrying Value $ 5,518.0 $ 5,342.0
Accumulated Amortization 4,673.4 4,453.4
Total acquired intangible assets    
Finite-Lived Intangible Assets [Line Items]    
Gross Carrying Value 5,462.1 5,290.3
Accumulated Amortization 4,628.3 4,412.9
Developed technology    
Finite-Lived Intangible Assets [Line Items]    
Gross Carrying Value 4,567.0 4,411.0
Accumulated Amortization 3,834.0 3,649.5
In-process research and development    
Finite-Lived Intangible Assets [Line Items]    
Gross Carrying Value 25.1 25.7
Accumulated Amortization 0.0 0.0
Customer relationships    
Finite-Lived Intangible Assets [Line Items]    
Gross Carrying Value 609.7 600.0
Accumulated Amortization 569.8 550.6
Trade names    
Finite-Lived Intangible Assets [Line Items]    
Gross Carrying Value 260.3 253.6
Accumulated Amortization 224.5 212.8
Internal-use software    
Finite-Lived Intangible Assets [Line Items]    
Gross Carrying Value 25.7 24.0
Accumulated Amortization 20.5 17.8
Capitalized software embedded in products    
Finite-Lived Intangible Assets [Line Items]    
Gross Carrying Value 30.2 27.7
Accumulated Amortization $ 24.6 $ 22.7