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Goodwill and Indefinite-Lived Intangible Assets (Narrative) (Details) - USD ($)
$ in Millions
12 Months Ended
Sep. 30, 2020
Sep. 30, 2019
Sep. 30, 2018
Finite-Lived Intangible Assets [Line Items]      
Amortization of Intangible Assets $ 118.2 $ 132.7 $ 117.9
Capitalized Computer Software, Amortization 9.2 10.3 $ 11.1
Finite-Lived Intangible Assets, Accumulated Amortization 667.3 597.0  
Indefinite-lived intangible assets $ 434.0    
Minimum [Member]      
Finite-Lived Intangible Assets [Line Items]      
Finite-Lived Intangible Asset, Useful Life 1 year    
Maximum [Member]      
Finite-Lived Intangible Assets [Line Items]      
Finite-Lived Intangible Asset, Useful Life 20 years    
Software and Software Development Costs [Member] | Minimum [Member]      
Finite-Lived Intangible Assets [Line Items]      
Finite-Lived Intangible Asset, Useful Life 3 years    
Software and Software Development Costs [Member] | Maximum [Member]      
Finite-Lived Intangible Assets [Line Items]      
Finite-Lived Intangible Asset, Useful Life 10 years    
Customer Relationships [Member]      
Finite-Lived Intangible Assets [Line Items]      
Finite-Lived Intangible Assets, Accumulated Amortization $ 358.7 333.8  
Developed Technology Rights [Member]      
Finite-Lived Intangible Assets [Line Items]      
Finite-Lived Intangible Assets, Accumulated Amortization $ 116.5 $ 79.5