P.S. My TI-36X Pro calculator gives Domain Error for 0^0. NARS2000 APL gives 1 for 0^0.

]]>( https://www.scratchjr.org/ )

( https://www.heise.de/ct/ausgabe/2017-9-Mit-ScratchJr-kurze-Animationen-zusammenklicken-3676917.html ) ]]>

Assad-

**Programmable Robotics for Logo-style learning…**

- 1/ Edison ($50 programmable robot) – https://meetedison.com/
- 2/ Roamer (£110 programmable robot) – http://www.valiant-technology.com/shop/shop.php?id=0id0&cat=10
- 2a/ This site has a ton of cool accessories and sensor expansion packs for Roamer.
- 2b/ This site has more details on Roamer robotics in usage.
- 2c/ This site has historic archives, from 1969 onwards.
- 3/ Simulation RC Turtle ($10) – I wonder if this one could be hacked, either with programmable software, or re-use the cool exterior over either the Edison (above) or a DIY motor base…
- 4/ Beebot Educational Robot (£50) – http://www.tts-group.co.uk/bee-bot-rechargeable-floor-robot/1001794.html
- 5/ mOway Robots – http://data-harvest.co.uk/catalogue/technology/secondary/moway-robots/secondary-moway-robots
- 6/ Makey Monkey ($50) – http://makeymakey.com/
- 7/ Mbot – http://www.makeblock.com/product/mbot-robot-kit

This is made by the same company, Valiant Technologies, that created the first physical Turtle that could be controlled with Logo.

In the US: https://www.bee-bot.us/

Using makey monkey you can interface common household objects to control your computer…

First – great website and resource.

Second – I would like to buy my neice a Turtle (works remotely) that she can use when learning logo. Which one and where do you recommend I get it?

Thanking you.

Myron

]]>Sid’s argument:

“We will assume that x^0 = 1 for all numbers x and show that this leads to a contradiction.

We know that 1 > -1.

But taking 0th powers of both sides and apply the assumption does not preserve the inequality, i.e. 1^0 = 1 = (-1)^0.

So the assumption is shown not to hold for any x, so in particular 0^1 cannot be 1.”

The two (fatal) flaws are:

1) the first line is in fact a provably true statement when x is non-zero. (Proof: x^(1-1) = x^1 x^-1 = x/x = 1, each of which holds for all x != 0)

2) taking powers does not preserve inequality (Consider 1 > -1 but 1^2 is not > than (-1)^2.) So even a failure here would not generate the desired contradiction.

Hope that helps. (But good effort in writing up an argument.)

Assad–

]]>Wouldn’t any number^0 be 0″? As it wouldn’t make sense if not?

For example

Let’s look at the statement

0+1>0-1

Now let’s say one decides to put this in parentheses

(0+1)>(0-1)

Now what if we make both sides (parenthesis) have to be to the power of 0

(0+1)^0>(0-1)^0

Which in turn simplifies to

(1)^0>(-1)^0

Making

1>1?

This can’t be true no matter what

1=1

But if x^0=0 then this statement would be valid, right?

On a tablet, this would probably be even more accessible to children, as the icons are suggestive, and replace remembering key-presses.

Thanks for sharing!

]]>http://www.logointerpreter.com/turtle-editor.php

– Stefan

]]>I wrote some lines for the file “interturtle.txt” using this feature:

start ;

start == init penup 250 -250 moveto pendown 90 rad turnto

; == dup (to copy the last drawing) dup ‘pen dictget [turtle] [] if draw

turtle == 1 pensize red pencolor 120 rad turn 12 move 210 rad turn 20 move -120 rad turn 20 move 210 rad turn 11 move

red == 255

black == 0

So there is no need for “next”:

( ** new Demo Program ** )

start ;

go ;

square ;

spin ;

square ;

spin ;

6 [square ; spin ; ] times

(penup ; ) (and the turtle is hide.)

– Stefan

]]>`next`

and `;`

– Assad

black == 0

white == 16777215

red == 255

go == penup 100 -100 moveto pendown 90 rad turnto

square == 4 [50 move 90 rad turn] times

spin == -45 rad turn penup 50 move pendown

```
```turtle == 120 rad turn 12 move 210 rad turn 20 move -120 rad turn 20 move 210 rad turn 11 move -60 rad turn penup 10 move pendown black pencolor

show-turtle == penup -10 move pendown red pencolor 1 pensize turtle dup draw

erase-turtle == penup -10 move pendown 3 pensize white pencolor turtle dup draw 1 pensize

next == erase-turtle

; == show-turtle

clearscreen == init draw

`( ** Demo Program ** )`

clearscreen

init go ;

next square ;

next spin ;

next square ;

next spin ;

6 [next square ; next spin ; ] times

]]>

Example in mjoy:

init penup 200 -200 moveto pendown 12 [30 square] stern draw

(init penup 200 -200 moveto pendown 12 [30 triangle] stern draw)

(init penup 200 -200 moveto pendown 12 [15 circle] stern draw)

stern == rotate 2 index [70 move -45 rad turn 3 index i 45 rad turn penup -70 move pendown 360 3 index / rad turn] times [pop pop] dip

triangle == swap 3 [2 index move 120 rad turn] times swap pop

square == swap 4 [2 index move 90 rad turn] times swap pop

Greetings, Stefan

]]>init penup 100 -100 moveto pendown 0 turnto house penup 200 -100 moveto pendown 0 turnto church draw

triangle == 25 20 moverel 25 -20 moverel -50 0 moverel

square-leg == 50 move 90 rad turn

square == 4 [square-leg] times

house == triangle -90 rad turn square

xtriangle == swap 3 [2 index move 120 rad turn] times swap pop

xsquare == swap 4 [2 index move 90 rad turn] times swap pop

church == 70 xtriangle -90 rad turn 70 xsquare

It can be saved in a textfile.

– Stefan

Would you be interested in writing out the specific user-oriented drawing instructions for mjoy? These could show through simple examples how to draw basic elements (point, segment, triangle, square, circle). German is fine, and I’m happy to test and translate to English.

Regards, Assad

]]>So I have suggested one of my programs, but your program / concept is for your

intentions (for preschoolers) much better than mine.

(Yes, I tried Turtle-Logo-Forth, for my personal testing.)

– Stefan ]]>

Do you have user-oriented instructions? Can be helpful to explain through a simple example, e.g:

To draw a triangle:

100 -100 moveto

pendown 10 pensize

10 20 moverel

90 rad turn

10 -20 moverel

45 rad turn

20 0 moverel

draw

or

To draw a square:

square-leg == 50 move 90 rad turn

square == square-leg 4 times

pendown square penup

Have you tried the Turtle-Logo-Forth above?

The equivalent of the above in my application would be (indicating key presses)

R fwd fwd fwd right right R ( this records the square-leg into diary 1 )

D ( this changes to diary 2 )

R 1 1 1 1 R ( this records 4 square legs into diary 2 )

2 ( draws square by calling diary-2 which calls diary-1 )

The commands are key-press driven, with immediate visual feedback. So the child sees coming alive the algorithm by which a square is constructed from 4 legs.

This kind of visual algorithmic construction is, in my view, a precursor to directly programming the turtle in the command line. I suspect even at 7 years, the delay to type and debug commands might be a barrier for entry.

Would be interesting to know how your nephew reacts.

Assad-

]]>It might be helpful to know that the turtle (dict) is an object, lying on the stack. In mjoy every data is local on the stack, except the constants (definitions).

In the file “Dokumentation.rtf” you can read something to the syntax of mjoy, in “Referenz.rtf” is something to the parameters. – Stefan

]]>But this also raises the complexity to learn to use it (took me a few hours of trial and error to figure out the syntax, and not totally there yet).

What’s been your observation of children using mjoy? – Assad

]]>You can find it under: https://www.heise.de/download/product/mjoy

Joy is a little bit like Forth. You may like it.

Greetings, Stefan ]]>

If x =0, it would be undefined due to people arguing about whether or not it should be 0 or 1.

So calculators can’t show 2 results and it can’t find out the answer, thus the errors

We should stop this fighting though, 0^0=1 makes not sense.

0^0=/= 0*0 which may cause confusion

X^1=X

X^0=1

But

0^0 is 0*unknown

So it’s should be 0 ]]>

part Thank you and good luck. ]]>

posts in this sort of area . Exploring in Yahoo I eventually stumbled upon this

site. Studying this information I am happy to say that I came upon just

what I needed. ]]>

You have some really good posts and I think I would be a good asset.

If you ever want to take some of the load off, I’d

absolutely love to write some articles for your blog, in exchange for a link back

to mine. Please send me an e-mail if interested.

Many thanks!

]]>It is sometimes claimed that defining 0^0=1 once and for all could lead to contradictions. This claim is wrong. It is based on a general distrust of 0, combined with faulty reasoning, such as: (a) arguments that require the impossible (requiring a discontinuous function to be continuous) or (b) arguments that use erroneous claims such as 0^x = 0 for all x (to see that this claim is wrong, try x=-1).

]]>any forums that cover the same topics discussed in this article?

I’d really love to be a part of online community where I can get comments from other

knowledgeable individuals that share the same interest.

If you have any recommendations, please let me know. Kudos!

]]>