Is it safe to assume RG6 cable strippers and cable connectors are going to be compatible?

I am planning to get a RG6 cable stripper and compression tool. Looking at Ebay there are some good deals but I am wondering if it is possible for the stripper and compression tool to be incompatible?
For example: If I get this compression tool:
http://cgi.ebay.com/ws/eBayISAPI.dll?ViewItem&itemX29879589&rd=1&sspagename=STRK%3AMEBI%3AIT&rd=1
and this stripper:
http://cgi.ebay.com/Coax-Cable-Stripping-Cutting-Tool-For-CATV-Directv-RG6_W0QQitemZ5830037596QQcategoryZ32840QQrdZ1QQcmdZViewItem
as long as they are used for RG6, they should be compatible - right? or no?
Thanks in advance,
MC
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They don't need to be compatible with each other, just the coax

http://cgi.ebay.com/ws/eBayISAPI.dll?ViewItem&itemX29879589&rd=1&sspagename=STRK%3AMEBI%3AIT&rd=1
http://cgi.ebay.com/Coax-Cable-Stripping-Cutting-Tool-For-CATV-Directv-RG6_W0QQitemZ5830037596QQcategoryZ32840QQrdZ1QQcmdZViewItem
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RBM wrote:

You need to make sure you have the proper connector for the _particular_ cable and the crimping tool for the connector. "RG6" isn't a sufficient description of the cable to spec connectors with.
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I have learned that there isn't a universal compression tool out there. Your connector needs to fit your compression tool.
We are eBay powersellers and we sell 2 different coax kits. The first one is a 3 in 1 compression tool + coax stripper + 25 - RG-6 Compression F Connectors. http://cgi.ebay.com/ws/eBayISAPI.dll?ViewItem&itemX30314216
The second kit is a 3 blade coax cable stripper, hex type F connector crimper and 50 - F connectors http://cgi.ebay.com/ws/eBayISAPI.dll?ViewItem&itemX22283357
We have sold ton of these kits on eBay and everyone just loves them. Be sure to check our feedback to see how satisfied our customers have been. Both of these kits are in stock and available for immediate shipment upon receipt of payment.
Please feel free to email us with questions about any of our products or services.
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