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Summary of Significant Accounting Policies - Schedule of Intangible Assets (Details) - USD ($) $ in Millions | Sep. 28, 2024 | Sep. 30, 2023
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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

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