> Your "counterexample" is not a normal number in any sense, most obviously because it isn't irrational, but only slightly less obviously because, as you note yourself, the sequences "321", "654", and "99" do not ever appear.
lol. Your counterargument is a tautology because it contains "the sequences "321", "654", and "99" do not ever appear."
It's like if you claim, "A has the property B" then I say, "based on this definition, I don't think A has property B"
Then you say, "if it doesn't have property B, then it's not A"
...okay, but my point is, the definition that I had (from wikipedia) doesn't imply B. So for you to say, "if it doesn't have B, then it's not A" is just circular.
Now, you can point out that the definition I got from wikipedia is different from the one you got from wolfram. That's fine. That's also true. And you can argue that the definition you used does indeed imply B.
But what you cannot do is use B as part of the definition, when that's the thing I'm asking you to demonstrate.
You: all christians are pro-life
Me: I don't see how that's true. Here's the definition of christianity. I don't see how it necessarily implies being against abortion.
You: your """"counterexample"""" (sarcastic quotes to show how smart I am) is obviously wrong because, as you note yourself, that person is pro-choice, therefore, not a christian.
^^^^^ do you see how this exchange inappropriately uses the thing you're being asked to prove, which is that christians are pro-life, as a component of the argument?
Again, it's totally cool if you fine a different definition of christian that explicitly requires they be pro-life. But given that I didn't use that definition, that doesn't make it the slam dunk you imagine.
> But given that I didn't use that definition, that doesn't make it the slam dunk you imagine.
You might have a better argument if there were more than one relevant definition of a normal number. As you should have read in the other responses to your comment, the definition given on wikipedia does not differ from the one given on Wolfram Alpha.
> And you can argue that the definition you used does indeed imply B.
Given that the implication of "B" is stated directly within the definition ("For example, ..."), this seemed unnecessary.
> but my point is, the definition that I had (from wikipedia) doesn't imply B. So for you to say, "if it doesn't have B, then it's not A" is just circular.
Look at it this way:
1. You provided a completely spurious definition, which you obviously did not get from wikipedia.
2. You provided a number satisfying your spurious definition, which - not being normal - didn't have the properties of a normal number.
3. I responded that you weren't using the definition of a normal number.
4. And I also responded that it's easy to see that the number you provided is not normal, because it doesn't have the properties that a normal number must have.
Try to identify the circular part of the argument.
And, consider whether it's cause for concern that you believe you got a definition of "normal number" from wikipedia when that definition of "normal number" is not available on wikipedia.
lol. Your counterargument is a tautology because it contains "the sequences "321", "654", and "99" do not ever appear."
It's like if you claim, "A has the property B" then I say, "based on this definition, I don't think A has property B"
Then you say, "if it doesn't have property B, then it's not A"
...okay, but my point is, the definition that I had (from wikipedia) doesn't imply B. So for you to say, "if it doesn't have B, then it's not A" is just circular.
Now, you can point out that the definition I got from wikipedia is different from the one you got from wolfram. That's fine. That's also true. And you can argue that the definition you used does indeed imply B.
But what you cannot do is use B as part of the definition, when that's the thing I'm asking you to demonstrate.
You: all christians are pro-life
Me: I don't see how that's true. Here's the definition of christianity. I don't see how it necessarily implies being against abortion.
You: your """"counterexample"""" (sarcastic quotes to show how smart I am) is obviously wrong because, as you note yourself, that person is pro-choice, therefore, not a christian.
^^^^^ do you see how this exchange inappropriately uses the thing you're being asked to prove, which is that christians are pro-life, as a component of the argument?
Again, it's totally cool if you fine a different definition of christian that explicitly requires they be pro-life. But given that I didn't use that definition, that doesn't make it the slam dunk you imagine.