There are various definitions that inappropriately define the concept of infinity, i.e., are responsible for at least 1 of the following:
Examples of inappropriate infinity definitions:
“without limits; extremely large or great.” – extremely large is typically used to refer to finite quantities, i.e., it implies there exists a size – but infinity is not a size; numerical value.
“extending indefinitely; endless.” – one definition of “indefinitely” is “unspecified”, which does not truly assert an infinite (limitless) state of existence.
Infinity (4 Definitions – this website uses 1 and 2 (technically 4 too) as defined below):
Finite: “limited in size or extent.”
Finitude: “the state of having limits or bounds.”
State: “the particular condition that someone or something is in at a specific time.”
Limitless: “without end, limit, or boundary.”
Continuous: “forming an unbroken whole; without interruption.”
Continuity: “the unbroken and consistent existence or operation of something over time.”
Continuum: “a continuous sequence in which adjacent elements are not perceptibly different from each other, but the extremes are quite distinct.”
Totality: “the whole of something.”
Infinitesimal: (American English): “too small to be measured; infinitely small.”
Numerical Value: “a real number regardless of its sign. absolute value. definite quantity – a specific measure of amount”
Normal Time: only the present exists, and time is simply the change of state of stuff, i.e., steps (increments) in time. If philosophically time is suggested to exist independent of changes in state, the analysis of an infinite number of changes in state remains the same, and therefore so does the paradoxical logic.
Normal Causality: the laws of physics simply playing out, i.e., each time step will result in a logical change of state.
Block Universe Time: there is no time in the normal way of thinking about it, simply because the past, present, and future, supposedly exist equally real.
Block Universe Causality: the laws of physics form the total state of existence all at once, i.e., there's effectively just 1 instant in time – no time. Theoretically it’s a direct result of time and distance not being absolute due to relativity theory.
Actualised: 1) Exists physically or has had an effect physically, 2) Already exists as a location in space – things that happened supposedly infinitely long ago and far away are actualised!
Chain of Causality: a given state cannot exist without being connected to its preceding state, unless it’s the 1st.
Potential-Infinity (A Misnomer): this term is oxymoronic! Not infinity at all, but simply changing in value, which can continue indefinitely – i.e., always existing as a finite value.
Countably-Infinite (A Misnomer): also an oxymoron, the same as potential infinity, but it’s sometimes used to assert the existence of different size infinite quantities of numbers – which is a contradiction in itself for the following two reasons: 1) Mathematical laws (so to speak) by themselves don’t actualise values into existence, 2) Infinity isn’t a numerical value, and therefore cannot be counted to.
Potential-Infinity & Countably-Infinite: physical laws (so to speak) such as those that allow the universe to expand indefinitely, and the mathematical laws that allow counting to continue indefinitely, cannot ever result in infinite values or existences.
The two terms in question can be extremely misleading to anybody trying to understand the logical meaning of infinity, i.e., limitless state of existence – the only plausible meaning with respect to the definition of: “Finite” as quoted in this website's definitions – hence why we use prefixes such as “in”.