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- SeeingColors
- Scratcher
500+ posts
Welcome to Scratch! Get started here!
Well I'm not a new Scratcher but hello to all of the new ones
- -Kawaii_Unicorn-
- Scratcher
6 posts
Welcome to Scratch! Get started here!
does being new to the forms count?
- oggy_250413
- Scratcher
10 posts
Welcome to Scratch! Get started here!
Hello, and have a warm welcome to Scratch!Welcome to Scratch, new Scratchers!
We're glad to have you as part of the community! We know how being new to something is like being lost in a forest at first, so I'm here to provide some tips and tricks on how to get involved with the Scratch community, and get to know everyone!
• A good way to get started in the community would be posting a topic in the New Scratchers forum. That will help you recognize some members in the community, and possibly meet new friends who will help you! Your topic doesn't have to be a long biography, you keep keep it short if that's what your comfortable with the most. For some ideas, you might want to check out this guide to Making a First Impression by ForeverArtist.
• A simple way to get familiar to the program would be just experimenting with the project editor! It's a good and quick way to discover the features quickly on your own. Who knows - You might create a fascinating project along the way! Never hurts to play around with the program for a while.
• Another good way to get involved with the community would be posting on the forums often. Helping others, posting on discussion threads, reporting glitches to the Scratch Team, all that can help you get involved!
• Don't be shy to ask anyone if you need to ask a question. All of us will be happy to help a New Scratcher in need, and will definitely do the best we can to help. If you are looking for help currently, good places to check out would be the following forums below:
- Help With Scripts: Need help with your Scratch project? Ask here!
- Requests: Looking for something? Want to offer your skills to others?
- Questions About Scratch: Post general questions about Scratch here.
• Here are some more great threads that you can look at to learn more about how the Scratch website works.
“Guidelines for the New Scratchers Forum” by Paddle2See (I recommend reading this before posting a thread in this forum.)
“Looking for Help in Discuss forums” by VectorHero
“All about ranks” by chocolatepenguin
“An explanation of the ”New Scratcher“ status” by jvvg
“BBCode Help” by nXIII
“How To Make EPIC Forum Signatures!” by kmeemaster (since moved to @TehCow)
“Why Scratch? A New Scratcher's Benefits Guide” by Haiming
“Achieving more followers (for New Scratchers)” by Hamish752
“Popularity - what is it, and is it important to become popular?” by Coder11000
"A guide to [Scratchblocks] and other BBCode help" by Techno-CAT
“Welcome to Scratch” by ZaharaMar
“Scratch: The Guide °Updated° Everything you need to know!” by makethebrainhappy
“Scratch Guide” by Evil_Leopard
“Remixing FAQ (Frequently Asked Questions” by Chibi-Matoran
“Profiles: A Guide ” by pastelistic
Good luck, and have fun Scratchin'!
Also, if you're not new, and just here to check this topic out, you can suggest additions to this topic, it'd be great!
- SlimeMaster952
- Scratcher
2 posts
Welcome to Scratch! Get started here!
Hi. This is my account where I work w/@graveheart on a game named suraimu.
Alt Accounts:
@EP912 (Main)
@ZOZOGOODDOG (Alt)
@Nobor2 (w/@rssa_romeo)
@EmePhe613 (OLDEST ACCOUNT Moved All Stuff to @EP912)
Best Friends:
@Nedaj1113
@graveheart
@rssa_romeo
@Superluigi1001
@joshanks
Alt Accounts:
@EP912 (Main)
@ZOZOGOODDOG (Alt)
@Nobor2 (w/@rssa_romeo)
@EmePhe613 (OLDEST ACCOUNT Moved All Stuff to @EP912)
Best Friends:
@Nedaj1113
@graveheart
@rssa_romeo
@Superluigi1001
@joshanks
Last edited by SlimeMaster952 (June 10, 2022 13:24:01)
- onu032001
- Scratcher
100+ posts
Welcome to Scratch! Get started here!
Just to get this out of the way, technically, ℵ1 is not the cardinality of the continuum. By definition, ℵ1 is simply the smallest cardinality greater than ℵ0 . The asertion that this is the cardinality of the continuum is known as the “continuum hypothesis”, and it cannot be proven or disproven with standard mathematical axioms.
Most introductions to fundamentals gloss over this fact, and assume the continuum hypothesis. And most people go on to assume that ℵ1 is in fact the cardinality of the continuum. Even math professors will get sloppy and implicitly make this assumption, leading you to believe that this is its true definition.
A lesser-known notation are the “beth numbers”. ℶ0 is identical to ℵ0 , and the cardinality of the continuum is, in fact, ℶ1 .
On to your question then, using beth numbers, as you intend.
By definition, ℶ1 is the number of possible functions from a set of cardinality ℶ0 to the set {0,1} .
With a little imagination and intuition, you can see that the real numbers in have cardinality ℶ1 . Any real number in this interval can be written in binary, and the binary representation can be interpreted as a function from natural numbers (the position) to {0,1} (the digit at that postion). And the reverse is true as well: any function from natural numbers to {0,1} can be interpreted as a binary fraction of a number in .
The next beth number, ℶ2 , is — as you might suspect — the cardinality of functions from a set of cardinality ℶ1 to the set {0,1} . So one example would be simply that: a set of functions of real numbers to {0,1} .
Yes, the beth numbers go on forever, as do the aleph-numbers. The continuum hypothesis asserts that ℶ1=ℵ1 , but at the very least, we know that ℶ1≥ℵ1 . Since the beth numbers go on forever, using the construction described above, we know that the aleph numbers also go on forever.
And it’s even better: since they go on infinitely, they can be indexed with infinte numbers! The indices of aleph and beth numbers are ordinal numbers. So you can have things like ℵω , ℵω+1 , ℵωω , ℵω1 , and stranger things still.
I personally lose track of any interpretations like ”continuums” or specific sets, long before that.
Most introductions to fundamentals gloss over this fact, and assume the continuum hypothesis. And most people go on to assume that ℵ1 is in fact the cardinality of the continuum. Even math professors will get sloppy and implicitly make this assumption, leading you to believe that this is its true definition.
A lesser-known notation are the “beth numbers”. ℶ0 is identical to ℵ0 , and the cardinality of the continuum is, in fact, ℶ1 .
On to your question then, using beth numbers, as you intend.
By definition, ℶ1 is the number of possible functions from a set of cardinality ℶ0 to the set {0,1} .
With a little imagination and intuition, you can see that the real numbers in have cardinality ℶ1 . Any real number in this interval can be written in binary, and the binary representation can be interpreted as a function from natural numbers (the position) to {0,1} (the digit at that postion). And the reverse is true as well: any function from natural numbers to {0,1} can be interpreted as a binary fraction of a number in .
The next beth number, ℶ2 , is — as you might suspect — the cardinality of functions from a set of cardinality ℶ1 to the set {0,1} . So one example would be simply that: a set of functions of real numbers to {0,1} .
Yes, the beth numbers go on forever, as do the aleph-numbers. The continuum hypothesis asserts that ℶ1=ℵ1 , but at the very least, we know that ℶ1≥ℵ1 . Since the beth numbers go on forever, using the construction described above, we know that the aleph numbers also go on forever.
And it’s even better: since they go on infinitely, they can be indexed with infinte numbers! The indices of aleph and beth numbers are ordinal numbers. So you can have things like ℵω , ℵω+1 , ℵωω , ℵω1 , and stranger things still.
I personally lose track of any interpretations like ”continuums” or specific sets, long before that.
- Sylveon5050
- Scratcher
2 posts
Welcome to Scratch! Get started here!
Helooo Well I'm not a new Scratcher but hello to all of the new ones
- BDAN2008
- Scratcher
3 posts
Welcome to Scratch! Get started here!
my game
coin clicker game https://scratch.mit.edu/projects/703274410
coin clicker game https://scratch.mit.edu/projects/703274410
- BDAN2008
- Scratcher
3 posts
Welcome to Scratch! Get started here!
my game
pong game https://scratch.mit.edu/projects/692724000
pong game https://scratch.mit.edu/projects/692724000
- scratchgodo
- Scratcher
1000+ posts
Welcome to Scratch! Get started here!
my game
coin clicker game Snip
Please advertise on the my game Show and Tell forum.
pong game Snip
King of the page.
Last edited by scratchgodo (June 11, 2022 11:06:50)
- KKmello
- Scratcher
2 posts
Welcome to Scratch! Get started here!
Hello Im New
Hey there! The scratch community welcomes you!
Hope you like the scratch community!
- KoolTheWizard91
- Scratcher
7 posts
Welcome to Scratch! Get started here!
Hello everyone, if any of you are new to scratch, then we suggest you click on the starter projects Scratch Team has for you. Make sure you click on ‘'Ideas’' to see what ideas the Scratch Team might have for you- KoolTheWzard91
when ‘'Ideas’' clicked
define"Scratch is for everyone!''
say for (2) secs
when ‘'Ideas’' clicked
define"Scratch is for everyone!''
say for (2) secs
- KoolTheWizard91
- Scratcher
7 posts
Welcome to Scratch! Get started here!
Well Scratch 2.0 is obsolete it can't be downloaded Hi my friends . I'm a new scratcher . I have a question ! How can I download scratch 2 (beta version) ? I would be very thankful if you could answer my question
- scratchgodo
- Scratcher
1000+ posts
Welcome to Scratch! Get started here!
That is not true see here.Well Scratch 2.0 is obsolete it can't be downloaded Hi my friends . I'm a new scratcher . I have a question ! How can I download scratch 2 (beta version) ? I would be very thankful if you could answer my question
- Avacac12078
- Scratcher
500+ posts
Welcome to Scratch! Get started here!
Been on Scratch for 1 year+, but this is still helpful
- skyraven2020
- Teacher
4 posts
Welcome to Scratch! Get started here!
Hi all, I'm new to the forum.
Just like to say thank you to let me join this fun and energetic community.
Just like to say thank you to let me join this fun and energetic community.