Other Intangible Assets and Goodwill Other Intangible Assets and Goodwill (Finite-Lived Intangible Assets) (Details) - USD ($) $ in Millions	3 Months Ended		6 Months Ended
	Apr. 01, 2018	Apr. 02, 2017	Apr. 01, 2018	Apr. 02, 2017	Oct. 01, 2017
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	$ 1,277.0		$ 1,277.0		$ 409.0
Accumulated amortization	(277.5)		(277.5)		(194.8)
Net carrying amount	999.5		999.5		214.2
Finite-Lived Intangible Assets, Amortization Expense, Next Twelve Months	58.8	$ 14.0	72.8	$ 28.5
Acquired and reacquired rights
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	1,174.5		1,174.5		328.8
Accumulated amortization	(232.1)		(232.1)		(154.2)
Net carrying amount	942.4		942.4		174.6
Acquired trade secrets and processes [Member]
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	32.0		32.0		27.6
Accumulated amortization	(18.3)		(18.3)		(13.7)
Net carrying amount	13.7		13.7		13.9
Trade Names, Trademarks and Patents [Member]
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	27.6		27.6		31.5
Accumulated amortization	(15.1)		(15.1)		(17.6)
Net carrying amount	12.5		12.5		13.9
Licensing Agreements [Member]
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	15.3		15.3		14.4
Accumulated amortization	(4.8)		(4.8)		(3.8)
Net carrying amount	10.5		10.5		10.6
Other finite-lived intangible assets [Member]
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	27.6		27.6		6.7
Accumulated amortization	(7.2)		(7.2)		(5.5)
Net carrying amount	$ 20.4		$ 20.4		$ 1.2