Will A Cash Less Society Result In Poor Mathematical Skills?

yes but math is more than counting. Did you know if there is a bijection between two ordinals (e.g. ω=1+ω and ω+1>ω), then they associate with the same cardinal. Any well-ordered set having an ordinal as its order-type has the same cardinality as that ordinal. The least ordinal associated with a given cardinal is called the initial ordinal of that cardinal.

Your question makes assumptions about current mathematical skill levels.

Does the diminishing popularity of paper money render schools incapable of using cash as a pedagogical tool? The fact that I don't use paper bills to buy my lunch doesn't mean that my school can't use cash to teach kids.

If I was you, I'd worry more about my own English skills rather than societies math skills. What is cash less? Maybe run more?

Walter Rudin Principles wrote:

Your question makes assumptions about current mathematical skill levels.

True. However, things can always get worse.

Mathematical skills, including those having to do with cash, are already a joke. Try giving a cashier $4.03 to pay for an item that rings up at $3.78 and watch the amazement on his/her face when he/she obediently punches in 4.03 and sees that you are magically owed a quarter. "How did you know that?"

amkelley wrote:

Mathematical skills, including those having to do with cash, are already a joke. Try giving a cashier $4.03 to pay for an item that rings up at $3.78 and watch the amazement on his/her face when he/she obediently punches in 4.03 and sees that you are magically owed a quarter. "How did you know that?"

Want to see a confused face? Ask a deli clerk for two thirds of a pound of something.

sliced ham wrote:

Want to see a confused face? Ask a deli clerk for two thirds of a pound of something.

OK, I'll start by putting some ham on the scale. There, it's 0.5 pounds (1/2)

So I add some more. OK, now 0.75 (3/4).

So I subtract some to get 0.625 (5/8), then add to get 11/16. subtract for 21/32, ...

When do you want me to stop?

Cash less?

How about poor english skills?

We, as a global society, are doomed, for the vast majority of humans cannot fathom one iota behind the simple fact that the category Nat(Hom(-,A), G) of natural transformations from the category Hom(-,A) of hom-functors into any object A of a fixed locally small category C to any covariant functor G from C to Set is isomorphic to G(A).

Mornas.

Anyone who has kids in public school knows that teachers do not employ active teaching methods in the classroom. Therefore, my prediction is that kids today will learn math as well as they ever have in the past (i.e., not well). School-aged children in the United States have very poor numerical literacy skills relative to the rest of the developed world. It really is mind boggling considering the amount of federal/state money that is poured into our schools. This statistic probably speaks more to issues inherent with teacher tenure – why bother yourself with engaging children in active learning projects when you can float by and dispense information in a passive manner? In most affluent communities, parents will compensate for the teacher's inadequate methods and schools know it.

anti moran wrote:

We, as a global society, are doomed, for the vast majority of humans cannot fathom one iota behind the simple fact that the category Nat(Hom(-,A), G) of natural transformations from the category Hom(-,A) of hom-functors into any object A of a fixed locally small category C to any covariant functor G from C to Set is isomorphic to G(A).

Mornas.

Most of us are too busy discussing under what conditions the isomorphism is canonical.

Diagram chaser wrote:

anti moran wrote:

We, as a global society, are doomed, for the vast majority of humans cannot fathom one iota behind the simple fact that the category Nat(Hom(-,A), G) of natural transformations from the category Hom(-,A) of hom-functors into any object A of a fixed locally small category C to any covariant functor G from C to Set is isomorphic to G(A).

Mornas.

Most of us are too busy discussing under what conditions the isomorphism is canonical.

morna

vacuous strawman

Those discussing sufficient conditions for a canonical iso are disjoint from those who do not understand the basic contravariant yoneda

morans

furthermore, arithmetic is not mathematics

in any way

We, as a global society, are doomed, for the vast majority of humans cannot fathom one iota behind the simple fact that the category Nat(Hom(-,A), G) of natural transformations from the category Hom(-,A) of hom-functors into any object A of a fixed locally small category C to any covariant functor G from C to Set is isomorphic to G(A).

If our global society is assuming the existence of a Grothendieck universe as a crutch, we are indeed doomed.

Strongly Inaccessible wrote:

We, as a global society, are doomed, for the vast majority of humans cannot fathom one iota behind the simple fact that the category Nat(Hom(-,A), G) of natural transformations from the category Hom(-,A) of hom-functors into any object A of a fixed locally small category C to any covariant functor G from C to Set is isomorphic to G(A).

If our global society is assuming the existence of a Grothendieck universe as a crutch, we are indeed doomed.

I doubt nothing Alex produced.

I live in a Grothendieck universe, so one exists.

MacLane doesn't require a Grothendieck universe, and everything can be formulated in terms of Gödel-Bernays and proper classes (and therein is usually what a "small" category means in the first place, that neither objects nor morphisms is a proper class).

OTOH, in the 70s, Sol Feferman had a category theory version of Quine's much-maligned New Foundations where the Yoneda Lemma was not provable (I don't know if he considered forcing or the consistency strength on the matter, as the reverse mathematics program as per Simpson was not vogue at the time, but NF with urelements is consistency-equivalent to Z).

It would result in complete control and domination of your life by the banking class and government. Everything you do will be recorded and the information can/will be used against you. If you don't conform to their will, your accounts can/will be frozen and you will be completely screwed. Aside from those things, new banking "tools" will be implemented resulting in fees you can't escape from, including bank bail-ins, negative interest rates, etc. etc.

Math will be the least of your problems. Enjoy your cashless society.

Mud wrote:

It would result in complete control and domination of your life by the banking class and government. Everything you do will be recorded and the information can/will be used against you. If you don't conform to their will, your accounts can/will be frozen and you will be completely screwed. Aside from those things, new banking "tools" will be implemented resulting in fees you can't escape from, including bank bail-ins, negative interest rates, etc. etc.

Math will be the least of your problems. Enjoy your cashless society.

Venezuela has started weighing cash instead of counting it.