Read the definition that you quoted more carefully. It does not state, "A number greater than any number," which would indeed be contradictory. Instead, it states, "A number greater than any assignable quantity or countable number," which is not contradictory at all.So that is:
- It's a number
AND
- It's greater than any number
The two are contradictory. — Devans99
A triangle cannot be a number. Does that mean geometry is not mathematics?Infinity can’t be a number. So it is not maths. — Devans99
It's a defective definition, thus not good for anything including posts about it. — tim wood
It's the commonly used definition. What definition would you give of infinity? — Devans99
Read the definition that you quoted more carefully. It does not state, "A number greater than any number," which would indeed be contradictory. Instead, it states, "A number greater than any assignable quantity or countable number," which is not contradictory at all — aletheist
But infinity cant't be bigger than any number because then it would not be a number. That's the mother of all contradictions.
So all the stuff about transfinite numbers and one-to-one correspondence is built on a nonsense definition of a nonsense concept. — Devans99
greater than any assignable quantity or countable number — Devans99
The author of the definition that you quoted would presumably reply: It is an infinite number.If a number is neither assignable or countable; then what sort of a number is it? — Devans99
Once again, you are smuggling in an additional premise--in this case, that something must be assignable or countable in order to qualify as a number.It is not a number. — Devans99
A triangle cannot be a number. Does that mean geometry is not mathematics?Infinity can’t be a number. So it is not maths. — Devans99
The author of the definition that you quoted would presumably reply: It is an infinite number. — aletheist
Once again, you are smuggling in an additional premise--in this case, that something must be assignable or countable in order to qualify as a number — aletheist
A triangle cannot be a number. Does that mean geometry is not mathematics? — aletheist
But infinity cant't be bigger than any number because then it would not be a number. That's the mother of all contradictions. — Devans99
An infinite number is a number bigger than any assignable quantity or countable number ... no contradiction.An infinite number is a number bigger than any number... same contradiction. — Devans99
Your original statement implied that only numbers belong in mathematics, so this is an improvement.Logical concepts only I would argue should be in maths. — Devans99
What is not logical is the claim that "1+∞ = ∞ implies 1 = 0"; it reveals an utter lack of understanding about the mathematics of infinity, which at this point is clearly willful.1+∞ = ∞ implies 1 = 0 is not logical. — Devans99
What is not logical is the claim that "1+∞ = ∞ implies 1 = 0"; it reveals an utter lack of understanding about the mathematics of infinity, which at this point is clearly willful — aletheist
What is not logical is the claim that "1+∞ = ∞ implies 1 = 0"; it reveals an utter lack of understanding about the mathematics of infinity, which at this point is clearly willful. — aletheist
Once again, you are smuggling in an additional premise--in this case, that something must be a quantity in order to qualify as a number.How can a quantity not change when you add another positive quantity to it? Thats impossible so infinity is not a quantity. — Devans99
Unfortunately, reading and knowledge do not necessarily translate to understanding. You have yet to identify a single contradiction when the relevant terms are defined consistently, and a paradox is simply an opportunity to think more carefully.I know plenty about the maths of infinity thank you. I have spent much time reading up on it. It's shot through with contradictions and paradoxes. — Devans99
So is logic, apparently; among other things, it requires being explicit about one's premises and consistent in one's use of terminology and definitions.Math is hard. — Rank Amateur
there are no infinite numbers. There is no greatest number (because X+1>X), so there can be no number larger than any finite number. — Devans99
I am not using colloquial definitions; I'm doing my best to be logical about it (unlike Cantor).
You have yet to identify a single contradiction when the relevant terms are defined consistently, and a paradox is simply an opportunity to think more carefully. — aletheist
How many numbers are there? How many square numbers are there? Unless you can answer those two questions, you cannot assert that one is greater than the other. Note that we are not talking about any finite interval, we are talking about all numbers and all square numbers.There are more numbers than there are square numbers yet each number has a square. — Devans99
See, the only thing contradictory in this entire discussion is your childish insistence on repeatedly applying the axioms of finite mathematics to infinity. Your "induction" here is straightforwardly false.We know by induction that there are more numbers than square numbers in all finite intervals so we can induce this implies to infinity as a whole. — Devans99
Indeed, an underlying logic error by the person who thinks that a paradox entails a contradiction.BTW A paradox is usually indicative of an underlying logic error. — Devans99
How many numbers are there? How many square numbers are there? — aletheist
See, the only thing contradictory in this entire discussion is your childish insistence on repeatedly applying the axioms of finite mathematics to infinity. Your "induction" here is straightforwardly false. — aletheist
Why? The fact of the matter is that it does not, so we can either throw up our hands (like you do) or find and develop meaningful alternatives (like mathematicians have).... the rest of maths obeys the arithmetic operators (or appropriate variations of them), infinity should too. — Devans99
Why is another example required to justify the one that we have been discussing? The whole point is that the mathematics of finite quantities are (rather obviously) not applicable to infinity.I challenge you to come up with another mathematical 'number' that you can add a non-zero amount to without changing? — Devans99
Why? The fact of the matter is that it does not, so we can either throw up our hands (like you do) or find and develop meaningful alternatives (like mathematicians have). — aletheist
The two are contradictory. Infinity can’t be a number. So it is not maths. — Devans99
Indeed, infinity is different from any finite quantity. So what? That does not make it illogical or contradictory, just different — aletheist
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