The human brain has a finite memory, thus the same limitations of a computer.

Sure, that's certainly true today. Computers are artificial and so, for the future, it will depend on what will be considered a computer.

To 'reach' or 'approach' "infinity' is a contradiction.

You cannot get closer to something that is a not accessible.

If infinity means "without end", "access" here means counting from any finite number to infinity and "counting" means counting like we count integers, then, yes, counting to infinity is a logical contradiction. There's no end to count up to.

------The basic issue

After experiencing forum debates (about 12 yrs) on supposedly settled issues, I questioned the concepts taught by 'experts' via teachers and publications. "Infinity" is the most annoying and misinterpreted concept.

It's a math issue resulting from poor grammatical structure.

It's not a math issue. It's up to people who argue about the infinite to specify what they mean, something most people don't do.

And it's not a "

*grammatical*" issue but an etymological issue and a logical one.

The mathematicians who defined limits should have consulted a dictionary.

I'm sure they did.

Dictionaries are not prescriptive but descriptive. They describe how words are used, they don't prescribe how they should be used. In effect, we are free to make up our own meaning and see if other people use it. That's what mathematicians do and it's what everybody does. And it's been like this since the beginning of words. Dictionaries came much later.

And you can look up a dictionary today and see that infinity in the mathematical sense is there:

Infinity

4. *Mathematics* The limit that a function ƒ is said to approach at *x* = *a* when *ƒ(x)* is larger than any preassigned number for all *x* sufficiently near *a.*

That's not very well formulated but we can understand what mathematicians mean and that's OK. There's certainly nothing illogical in the idea of an infinite limit in this sense.

'Infinity' defined as "without limit" cannot be used as a quantifier, i.e. it's immeasurable. It's not just about numbers, but a property of any collection of elements. Since it was represented by a symbol, many want to treat it as a number.

The Peano method of integer formation by adding a defined unit to a set of symbols is an abstraction. The symbols are representations of things, therefore the method does not imply a physical reality to an unlimited set of things.

Words are abstractions, too. No word we use could possibly entail the reality of what the word is supposed to refer to. That's true of all our ideas about the material world. Now, I don't think we want to stop talking about the material world as if we knew what it is.

By definition, an 'infinite' list has no end, therefore it is independent of time.

I'm not sure without time anything would exist. But maybe it's the other way round, time maybe is just the counting of what things do.

On substance, it seems possible to reach infinity because, apparently, that's something we do all the time. Again, just because we can conceive of infinity as something we can reach doesn't entail the existence of this kind of infinity but this in turn doesn't entail that this kind of infinity doesn't exist. All we can do is try and ensure we remain logical in our ideas. Logical ideas seem to tell us what we can try in practice without fear of getting hurt.

And of course, that we're unable to count an infinite number of anything like we can count our five fingers doesn't entail there isn't an infinite number of anything.

Personally, I can conceive of an infinity which has a limit, or even several limits, or even an infinity of limits. I fail to see where there would be a logical contradiction in that.

EB