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If you want the public to be able to read your wiki, check View for Anonymous Access.
If you want the public to be able to edit your wiki (this is not advisable as it attracts spam page/comment adds), check Add (under Pages) for Anonymous Access.
Please note that public users do not have accounts, so all edits will be listed as created/done by Do not check any other options for for Anonymous Access - this allows any user, even those not logged in, to make changes to your wiki space. There is no way to track these changes as all edits by non-logged in users are attributed to Anonymous.
Once the appropriate permissions have been checked for the groups or individuals, click Save All.
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