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Goodwill and Purchased Intangible Assets - Schedule of Purchased Intangible Assets (Details) - USD ($) $ in Millions | 12 Months Ended
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Sep. 30, 2020 | Sep. 30, 2019
Acquired Finite Lived Intangible Assets [Line Items] |  |
Weighted- Average Life (in years) | 14 years 8 months 12 days | 14 years 8 months 12 days
Gross | $ 731.2 | $ 731.2
Accumulated Amortization | (697.7) | (686.6)
Net | 33.5 | 44.6
Non-amortizable trade names | 384.7 | 387.7
Intangible assets excluding goodwill, gross | 1,115.9 | 1,118.9
Purchased intangible assets, net | $ 418.2 | $ 432.3
Distribution network |  |
Acquired Finite Lived Intangible Assets [Line Items] |  |
Weighted- Average Life (in years) | 39 years 1 month 6 days | 39 years 1 month 6 days
Gross | $ 55.4 | $ 55.4
Accumulated Amortization | (33.8) | (32.3)
Net | $ 21.6 | $ 23.1
Technology-related |  |
Acquired Finite Lived Intangible Assets [Line Items] |  |
Weighted- Average Life (in years) | 11 years 10 months 24 days | 11 years 10 months 24 days
Gross | $ 104.7 | $ 104.7
Accumulated Amortization | (103.3) | (102.6)
Net | $ 1.4 | $ 2.1
Customer relationships |  |
Acquired Finite Lived Intangible Assets [Line Items] |  |
Weighted- Average Life (in years) | 12 years 9 months 18 days | 12 years 9 months 18 days
Gross | $ 554.7 | $ 554.8
Accumulated Amortization | (545.6) | (536.8)
Net | $ 9.1 | $ 18.0
Other |  |
Acquired Finite Lived Intangible Assets [Line Items] |  |
Weighted- Average Life (in years) | 16 years 3 months 18 days | 16 years 1 month 6 days
Gross | $ 16.4 | $ 16.3
Accumulated Amortization | (15.0) | (14.9)
Net | $ 1.4 | $ 1.4

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