Goodwill and Intangible Assets, Net - Components and Reconciliation of Goodwill (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Jul. 02, 2017	Jul. 03, 2016	Jul. 02, 2017	Jul. 03, 2016	Jul. 02, 2017	Oct. 02, 2016
Goodwill and Intangible Assets Disclosure [Line Items]
Amortizable intangible assets					$ 759.0	$ 693.6
Goodwill	$ 2,500.4		$ 2,479.4		2,500.4	2,479.4
Goodwill [Roll Forward]
Balance as of October 2, 2016			2,479.4
Adjustments from acquisitions and divestitures			21.0
Balance as of July 2, 2017	2,500.4		2,500.4
Amortization of intangible assets	49.6	$ 44.9	141.6	$ 115.6
Completed technology
Goodwill and Intangible Assets Disclosure [Line Items]
Amortizable intangible assets					671.8	572.6
Goodwill [Roll Forward]
Amortization of intangible assets	38.0	32.4	104.1	76.9
Customer relationships
Goodwill and Intangible Assets Disclosure [Line Items]
Amortizable intangible assets					87.1	118.8
Goodwill [Roll Forward]
Amortization of intangible assets	11.6	11.6	35.3	34.5
Backlog, trade name and other
Goodwill and Intangible Assets Disclosure [Line Items]
Amortizable intangible assets					0.1	2.2
Goodwill [Roll Forward]
Amortization of intangible assets	$ 0.0	$ 0.9	$ 2.2	$ 4.2
In-process research and development
Goodwill and Intangible Assets Disclosure [Line Items]
Non-amortizable intangible assets					$ 41.0	$ 241.0