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My son, also 6 yo, regularly talks about millions and billions and infinity. Obviously, large numbers have some attraction to children of this age.

I try to explain that infinity is not a number. Instead, infinity is an order of magnitude which has its own algebraic rules. Plus, minus, divison and multiplication do not work the way children learn in elementary school when applied to infinity.

My first explanation is that this has also an impact on how we use the words infinity and infinite:

Three meters. (works)

 

*Infinity meters. (completely wrong)

 

*Infinite meters. (sounds wrong)

 

Infinitely many meters. (works)

Another approach is that the concept of numbers does not work. Numbers grow. For every number, there is another number that is larger. The mathematical notation to this concept is $\forall n \in \mathbb{N}: \exists m \in \mathbb{N}: m > n$. If infinity was a number, then this statement would be false, because let $n=\infty$, then $\infty + m > \infty$ is false for all $m \in \mathbb{N}$ where $m > 0$. Surprisingly, children who already learnt addition upto, say, 100, understand this. They understand that 100 is not the largest of all numbers, neither is 1000, neither is a million, and so on. But the fact, that addition does not alter the "number", makes them understand that infinity is not a number.

In words that are better suited for children, you can also say: Adding any number to infinity does not change its size, because infinity expresses a magnitude, a size, rather than a number.

Admittedly, my daughter, 8 yo, understands this point better, because my 6 yo son has not yet learnt addition of numbers larger than his 10 fingers provide.

My son, also 6 yo, regularly talks about millions and billions and infinity. Obviously, large numbers have some attraction to children of this age.

I try to explain that infinity is not a number. Instead, infinity is an order of magnitude which has its own algebraic rules. Plus, minus, divison and multiplication do not work the way children learn in elementary school when applied to infinity.

My first explanation is that this has also an impact on how we use the words infinity and infinite:

Three meters. (works)

*Infinity meters. (completely wrong)

*Infinite meters. (sounds wrong)

Infinitely many meters. (works)

Another approach is that the concept of numbers does not work. Numbers grow. For every number, there is another number that is larger. The mathematical notation to this concept is $\forall n \in \mathbb{N}: \exists m \in \mathbb{N}: m > n$. If infinity was a number, then this statement would be false, because let $n=\infty$, then $\infty + m > \infty$ is false for all $m \in \mathbb{N}$ where $m > 0$. Surprisingly, children who already learnt addition upto, say, 100, understand this. They understand that 100 is not the largest of all numbers, neither is 1000, neither is a million, and so on. But the fact, that addition does not alter the "number", makes them understand that infinity is not a number.

In words that are better suited for children, you can also say: Adding any number to infinity does not change its size, because infinity expresses a magnitude, a size, rather than a number.

Admittedly, my daughter, 8 yo, understands this point better, because my 6 yo son has not yet learnt addition of numbers larger than his 10 fingers provide.

My son, also 6 yo, regularly talks about millions and billions and infinity. Obviously, large numbers have some attraction to children of this age.

I try to explain that infinity is not a number. Instead, infinity is an order of magnitude which has its own algebraic rules. Plus, minus, divison and multiplication do not work the way children learn in elementary school when applied to infinity.

My first explanation is that this has also an impact on how we use the words infinity and infinite:

Three meters. (works)

*Infinity meters. (completely wrong)

*Infinite meters. (sounds wrong)

Infinitely many meters. (works)

Another approach is that the concept of numbers does not work. Numbers grow. For every number, there is another number that is larger. The mathematical notation to this concept is $\forall n \in \mathbb{N}: \exists m \in \mathbb{N}: m > n$. If infinity was a number, than this statement would be false, because let $n=\infty$, then $\infty + m > \infty$ is false for all $m \in \mathbb{N}$. Surprisingly, children who already learnt addition upto, say, 100, understand this. They understand that 100 is not the end highest of all numbers, neither is 1000, neither is a million, and so on. But the fact, that addition does not alter the "number", makes them understand that infinity is not a number.

In words that are better suited for children, you can also say: Adding any number to infinity does not change its size, because infinity expresses a magnitude, a size, rather than a number.

Admittedly, my daughter, 8 yo, understands this point better, because my 6 yo son has not yet learnt addition of numbers larger than his 10 fingers provide.

My son, also 6 yo, regularly talks about millions and billions and infinity. Obviously, large numbers have some attraction to children of this age.

I try to explain that infinity is not a number. Instead, infinity is an order of magnitude which has its own algebraic rules. Plus, minus, divison and multiplication do not work the way children learn in elementary school when applied to infinity.

My first explanation is that this has also an impact on how we use the words infinity and infinite:

Three meters. (works)

*Infinity meters. (completely wrong)

*Infinite meters. (sounds wrong)

Infinitely many meters. (works)

Another approach is that the concept of numbers does not work. Numbers grow. For every number, there is another number that is larger. The mathematical notation to this concept is $\forall n \in \mathbb{N}: \exists m \in \mathbb{N}: m > n$. If infinity was a number, then this statement would be false, because let $n=\infty$, then $\infty + m > \infty$ is false for all $m \in \mathbb{N}$ where $m > 0$. Surprisingly, children who already learnt addition upto, say, 100, understand this. They understand that 100 is not the largest of all numbers, neither is 1000, neither is a million, and so on. But the fact, that addition does not alter the "number", makes them understand that infinity is not a number.

In words that are better suited for children, you can also say: Adding any number to infinity does not change its size, because infinity expresses a magnitude, a size, rather than a number.

Admittedly, my daughter, 8 yo, understands this point better, because my 6 yo son has not yet learnt addition of numbers larger than his 10 fingers provide.

My son, also 6 yo, regularly talks about millions and billions and infinity. Obviously, large numbers have some attraction to children of this age.

I try to explain that infinity is not a number. Instead, infinity is an order of magnitude which has its own algebraic rules. Plus, minus, divison and multiplication do not work the way children learn in elementary school when applied to infinity.

My first explanation is that this has also an impact on how we use the words infinity and infinite:

Three meters. (works)

*Infinity meters. (completely wrong)

*Infinite meters. (sounds wrong)

Infinitely many meters. (works)

Another approach is that the concept of numbers does not work. Numbers grow. For every number, there is another number that is larger. The mathematical notation to this concept is $\forall n \in \mathbb{N}: \exists m \in \mathbb{N}: m > n$. If infinity was a number, than this statement would be false, because let $n=\infty$, then $\infty + m > \infty$ is false for all $m \in \mathbb{N}$. Surprisingly, children who already learnt addition upto, say, 100, understand this. They understand that 100 is not the end highest of all numbers, neither is 1000, neither is a million, and so on. But the fact, that addition does not alter the "number", makes them understand that infinity is not a number.

In words that are better suited for children, you can also say: Adding any number to infinity does not change its size, because infinity expresses a magnitude, a size, rather than a number.

Admittedly, my daughter, 8 yo, understand this point better, because my 6 yo son had not yet learnt addition of numbers larger than his 10 fingers provide.

My son, also 6 yo, regularly talks about millions and billions and infinity. Obviously, large numbers have some attraction to children of this age.

I try to explain that infinity is not a number. Instead, infinity is an order of magnitude which has its own algebraic rules. Plus, minus, divison and multiplication do not work the way children learn in elementary school when applied to infinity.

My first explanation is that this has also an impact on how we use the words infinity and infinite:

Three meters. (works)

*Infinity meters. (completely wrong)

*Infinite meters. (sounds wrong)

Infinitely many meters. (works)

Another approach is that the concept of numbers does not work. Numbers grow. For every number, there is another number that is larger. The mathematical notation to this concept is $\forall n \in \mathbb{N}: \exists m \in \mathbb{N}: m > n$. If infinity was a number, than this statement would be false, because let $n=\infty$, then $\infty + m > \infty$ is false for all $m \in \mathbb{N}$. Surprisingly, children who already learnt addition upto, say, 100, understand this. They understand that 100 is not the end highest of all numbers, neither is 1000, neither is a million, and so on. But the fact, that addition does not alter the "number", makes them understand that infinity is not a number.

In words that are better suited for children, you can also say: Adding any number to infinity does not change its size, because infinity expresses a magnitude, a size, rather than a number.

Admittedly, my daughter, 8 yo, understands this point better, because my 6 yo son has not yet learnt addition of numbers larger than his 10 fingers provide.