Income Taxes (Summary of Activity Related to Unrecognized Tax Benefits) (Details) - USD ($) $ in Millions	12 Months Ended
	Oct. 01, 2023	Oct. 02, 2022	Oct. 03, 2021
Significant Change in Unrecognized Tax Benefits is Reasonably Possible [Line Items]
Beginning balance	$ 89.7	$ 82.6	$ 123.7
Increase related to prior year tax positions	1.2	0.2	4.8
Decrease related to prior year tax positions	(0.4)	(0.7)	(11.9)
Increase related to current year tax positions	14.5	9.0	8.9
Decreases related to settlements with taxing authorities	0.0	0.0	(4.4)
Decreases related to lapsing of statute of limitations	0.0	(1.4)	(38.5)
Ending balance	105.0	89.7	82.6
Gross unrecognized tax benefits	105.0	89.7	82.6
Unrecognized tax benefits affecting the effective tax rate if recognized	72.8
Interest and penalties expense/(benefit) recognized in income tax expense	5.7	(2.3)	$ (4.6)
Accrued interest and penalties	15.1	$ 9.4
Maximum [Member]
Significant Change in Unrecognized Tax Benefits is Reasonably Possible [Line Items]
Amount of reasonably possible unrecognized benefit change	$ 54.0